Estonian Land Board data

Available via www.maaamet.ee. API can be accessed programmatically using html requests. One can use “rvest” package. Please have a look at “R/maaamet.R” script in rstats-tartu/datasets repo. Returns html, but that ok too. Html results need little wrangling to get table.

Data that can be downloaded are number of transactions and price summaries per property size, and type for different time periods. Price info is given for data splits with more than 5 transactions.

Load dataset

##  Check if file is alredy downloaded 
if(!file.exists("data/transactions_residential_apartments.csv")){
  url <- "https://raw.githubusercontent.com/rstats-tartu/datasets/master/transactions_residential_apartments.csv"
  
  ## Check if data folder is present
  if(!dir.exists("data")){
    dir.create("data")
  }
  ## Download file to data folder
  download.file(url, "data/transactions_residential_apartments.csv")
}

Import

library(tidyverse)
## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr
## Conflicts with tidy packages ----------------------------------------------
## filter(): dplyr, stats
## lag():    dplyr, stats
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following object is masked from 'package:base':
## 
##     date
library(stringr)
# Please try broom from GitHub as CRAN version may give obscure warning
# with augment
# devtools::install_github("dgrtwo/broom")
library(broom)
library(viridis)
## Loading required package: viridisLite
apartments <- read_csv("data/transactions_residential_apartments.csv")
## Parsed with column specification:
## cols(
##   year = col_integer(),
##   month = col_character(),
##   county = col_character(),
##   area = col_character(),
##   transactions = col_integer(),
##   area_total = col_double(),
##   area_mean = col_double(),
##   price_total = col_integer(),
##   price_min = col_double(),
##   price_max = col_double(),
##   price_unit_area_min = col_double(),
##   price_unit_area_max = col_double(),
##   price_unit_area_median = col_double(),
##   price_unit_area_mean = col_double(),
##   price_unit_area_sd = col_double(),
##   title = col_character(),
##   subtitle = col_character()
## )
## Warning in rbind(names(probs), probs_f): number of columns of result is not
## a multiple of vector length (arg 1)
## Warning: 31 parsing failures.
## row # A tibble: 5 x 5 col     row         col               expected actual expected   <int>       <chr>                  <chr>  <chr> actual 1 11495 price_total no trailing characters     e3 file 2 11504 price_total no trailing characters     e3 row 3 11512 price_total no trailing characters     e3 col 4 11513 price_total no trailing characters     e3 expected 5 11573 price_total no trailing characters     e3 actual # ... with 1 more variables: file <chr>
## ... ................. ... ................................................. ........ ................................................. ...... ................................................. .... ................................................. ... ................................................. ... ................................................. ........ ................................................. ...... .......................................
## See problems(...) for more details.
apartments <- apartments %>% 
  mutate(date = ymd(str_c(year, month, 1, sep = "-"))) %>% 
  select(date, everything())
harju <- apartments %>% filter(str_detect(county, "Harju"))
harju
## # A tibble: 890 x 18
##          date  year month        county      area transactions area_total
##        <date> <int> <chr>         <chr>     <chr>        <int>      <dbl>
##  1 2005-01-01  2005   Jan Harju maakond  10-29,99           65     1418.8
##  2 2005-01-01  2005   Jan Harju maakond  30-40,99          155     5431.5
##  3 2005-01-01  2005   Jan Harju maakond  41-54,99          253    12043.8
##  4 2005-01-01  2005   Jan Harju maakond  55-69,99          230    14515.9
##  5 2005-01-01  2005   Jan Harju maakond 70-249,99          118    10905.0
##  6 2005-02-01  2005   Feb Harju maakond  10-29,99           63     1340.2
##  7 2005-02-01  2005   Feb Harju maakond  30-40,99          175     6125.2
##  8 2005-02-01  2005   Feb Harju maakond  41-54,99          257    12233.8
##  9 2005-02-01  2005   Feb Harju maakond  55-69,99          249    15659.0
## 10 2005-02-01  2005   Feb Harju maakond 70-249,99          174    15926.1
## # ... with 880 more rows, and 11 more variables: area_mean <dbl>,
## #   price_total <int>, price_min <dbl>, price_max <dbl>,
## #   price_unit_area_min <dbl>, price_unit_area_max <dbl>,
## #   price_unit_area_median <dbl>, price_unit_area_mean <dbl>,
## #   price_unit_area_sd <dbl>, title <chr>, subtitle <chr>

Strategy

  • Start with single unit and identify interesting pattern

  • Summarise pattern with model

  • Apply model to all units

  • Look for units that don’t fit pattern

  • Summarise with single model

First glimpse

Plot number of transactions per year for Harju county and add smooth line.

p <- ggplot(harju, aes(factor(year), transactions, group = area, color = area)) +
  geom_point() +
  geom_smooth(method = 'loess') +
  facet_wrap(~county, scales = "free_y") +
  labs(
    y = "Transactions",
    x = "Year"
  ) +
  scale_color_viridis(discrete = TRUE)
p

Mean price per unit area:

## Add date 
p <- harju %>%
  ggplot(aes(date, price_unit_area_mean, group = area, color = area)) +
  geom_line() +
  geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
  labs(title = "Transactions with residential apartments",
       subtitle = "Harju county",
       x = "Date",
       y = bquote(Mean~price~(eur/m^2)),
       caption = str_c("Source: Estonian Land Board, transactions database.\nDashed line, the collapse of the investment bank\nLehman Brothers on Sep 15, 2008.")) +
  scale_color_viridis(discrete = TRUE, name = bquote(Apartment~size~m^2))
p

Adjust mean price to changes in consumer index:

download.file("https://raw.githubusercontent.com/rstats-tartu/datasets/master/consumer_index.csv",
              "data/consumer_index.csv")
consumer_index <- read_csv("data/consumer_index.csv")
## Warning: Missing column names filled in: 'X1' [1]
## Parsed with column specification:
## cols(
##   X1 = col_integer(),
##   year = col_integer(),
##   Jan = col_double(),
##   Feb = col_double(),
##   Mar = col_double(),
##   Apr = col_double(),
##   May = col_double(),
##   Jun = col_double(),
##   Jul = col_double(),
##   Aug = col_double(),
##   Sep = col_double(),
##   Oct = col_double(),
##   Nov = col_double(),
##   Dec = col_double()
## )
consumer_index
## # A tibble: 22 x 14
##       X1  year   Jan   Feb   Mar   Apr   May    Jun    Jul    Aug    Sep
##    <int> <int> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl>
##  1     1  1996 61.86 63.84 64.90 66.02 66.35  66.74  66.94  66.28  66.55
##  2     2  1997 68.59 69.05 69.58 70.63 71.95  72.42  72.68  73.01  73.34
##  3     3  1998 76.50 77.23 77.89 78.22 78.48  78.68  79.14  79.01  78.88
##  4     4  1999 79.93 80.13 80.46 80.73 80.99  80.92  80.99  80.86  80.86
##  5     5  2000 82.37 82.44 83.03 83.10 83.23  83.50  84.29  84.35  84.68
##  6     6  2001 87.06 87.32 87.72 88.31 88.84  89.04  89.23  89.30  89.50
##  7     7  2002 90.75 91.28 91.54 92.33 92.53  92.46  92.14  91.74  91.87
##  8     8  2003 93.06 93.32 93.52 93.39 93.19  92.86  92.99  92.99  93.26
##  9     9  2004 93.65 93.85 94.18 94.77 96.62  96.95  96.69  96.62  96.82
## 10    10  2005 97.54 98.14 98.73 99.19 99.39 100.05 100.45 100.71 101.57
## # ... with 12 more rows, and 3 more variables: Oct <dbl>, Nov <dbl>,
## #   Dec <dbl>
## check if 2005 is 100%
consumer_index[10, 3:14] %>% rowMeans()
## [1] 100
divide_by_100 <- function(x) {
  x/100
  }
consumer_index <- consumer_index %>% 
  select(-X1) %>% 
  gather(key = month, value = consumerindex, -year) %>% 
  mutate_at("consumerindex", divide_by_100)
consumer_index
## # A tibble: 264 x 3
##     year month consumerindex
##    <int> <chr>         <dbl>
##  1  1996   Jan        0.6186
##  2  1997   Jan        0.6859
##  3  1998   Jan        0.7650
##  4  1999   Jan        0.7993
##  5  2000   Jan        0.8237
##  6  2001   Jan        0.8706
##  7  2002   Jan        0.9075
##  8  2003   Jan        0.9306
##  9  2004   Jan        0.9365
## 10  2005   Jan        0.9754
## # ... with 254 more rows

Join apartments and consumer index data:

apartments <- left_join(apartments, consumer_index, by = c("year", "month"))

Select harju county data:

harju_ci <- filter(apartments, str_detect(county, "Harju"))
harju_ci
## # A tibble: 890 x 19
##          date  year month        county      area transactions area_total
##        <date> <int> <chr>         <chr>     <chr>        <int>      <dbl>
##  1 2005-01-01  2005   Jan Harju maakond  10-29,99           65     1418.8
##  2 2005-01-01  2005   Jan Harju maakond  30-40,99          155     5431.5
##  3 2005-01-01  2005   Jan Harju maakond  41-54,99          253    12043.8
##  4 2005-01-01  2005   Jan Harju maakond  55-69,99          230    14515.9
##  5 2005-01-01  2005   Jan Harju maakond 70-249,99          118    10905.0
##  6 2005-02-01  2005   Feb Harju maakond  10-29,99           63     1340.2
##  7 2005-02-01  2005   Feb Harju maakond  30-40,99          175     6125.2
##  8 2005-02-01  2005   Feb Harju maakond  41-54,99          257    12233.8
##  9 2005-02-01  2005   Feb Harju maakond  55-69,99          249    15659.0
## 10 2005-02-01  2005   Feb Harju maakond 70-249,99          174    15926.1
## # ... with 880 more rows, and 12 more variables: area_mean <dbl>,
## #   price_total <int>, price_min <dbl>, price_max <dbl>,
## #   price_unit_area_min <dbl>, price_unit_area_max <dbl>,
## #   price_unit_area_median <dbl>, price_unit_area_mean <dbl>,
## #   price_unit_area_sd <dbl>, title <chr>, subtitle <chr>,
## #   consumerindex <dbl>
harju_ci <- harju_ci %>% 
  mutate(pua_mean_ci = price_unit_area_mean / consumerindex)

Price per m^2 after consumer index adjustment:

harju_ci %>%
  ggplot(aes(date, pua_mean_ci, group = area, color = area)) +
  geom_line() +
  geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
  labs(title = "Transactions with residential apartments",
       subtitle = "Harju county",
       x = "Date",
       y = "Consumer index corrected mean price\nrelative to 2005 (eur/m^2)",
       caption = str_c("Source: Estonian Land Board, transactions database.\nDashed line, the collapse of the investment bank\nLehman Brothers on Sep 15, 2008.")) +
  scale_color_viridis(discrete = TRUE, name = bquote(Apartment~size~m^2))

Seasonal pattern

Seasonal pattern in number of transactions? Mean price eur/m^2 per month:

## Note that we are rearranging x axis using R builtin vector of month names
p <- harju %>%
  ggplot(aes(factor(month, levels = month.abb), transactions, group = year)) +
  geom_line(alpha = 0.3) +
  geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
  facet_wrap(~ area, scales = "free_y") +
  labs(title = "Seasonal trend in number of transactions\nwith residential apartments",
       subtitle = "Harju county",
       x = "Month",
       y = "Transactions",
       caption = "Source: Estonian Land Board, transactions database.") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5))
p

Add trendline per month. Fit linear model per month for each apartment size class. augment() function from “broom” library adds fitted values and residuals to the original data. We can use this to overlay model fit to our data.

predicted_transa <- harju %>% 
  lm(transactions ~ month + area, data = .) %>%
  augment() # broom
predicted_transa %>% 
  arrange(desc(.cooksd)) %>% 
  dplyr::select(.cooksd, everything()) %>% 
  head
##      .cooksd transactions month     area  .fitted  .se.fit   .resid
## 1 0.02159508          530   Nov 41-54,99 258.5006 8.840215 271.4994
## 2 0.01811853          512   Oct 41-54,99 256.5092 8.613145 255.4908
## 3 0.01785884          461   Nov 55-69,99 214.1018 8.840215 246.8982
## 4 0.01776184          457   Dec 55-69,99 210.7732 8.840215 246.2268
## 5 0.01653771          492   Aug 41-54,99 247.9092 8.613145 244.0908
## 6 0.01528834          443   Sep 55-69,99 208.3103 8.613145 234.6897
##         .hat   .sigma .std.resid
## 1 0.01878010 63.87491   4.248853
## 2 0.01782772 63.95253   3.996386
## 3 0.01878010 63.99134   3.863856
## 4 0.01878010 63.99436   3.853348
## 5 0.01782772 64.00444   3.818068
## 6 0.01782772 64.04544   3.671015

Overlay fitted values to previous plot.

p + geom_line(data = predicted_transa, aes(month, .fitted, group = 1), 
              color = "red",
              size = 2) +
  labs(caption = "Red line: model fit of seasonal effect to number of transactions.\nSource: Estonian Land Board, transactions database.")

The number of transactions increases during period from March to May?

Do we have similar effect to average price per m^2?

predicted_pua <- harju %>% 
  lm(price_unit_area_mean ~ month + area, data = .) %>%
  augment()
predicted_pua %>% head
##   price_unit_area_mean month      area  .fitted .se.fit    .resid
## 1               766.69   Jan  10-29,99 1167.756 36.6406 -401.0660
## 2               738.23   Jan  30-40,99 1143.193 36.6406 -404.9631
## 3               719.91   Jan  41-54,99 1159.304 36.6406 -439.3937
## 4               699.59   Jan  55-69,99 1166.595 36.6406 -467.0046
## 5               886.06   Jan 70-249,99 1347.656 36.6406 -461.5959
## 6               705.96   Feb  10-29,99 1175.696 36.6406 -469.7363
##         .hat   .sigma     .cooksd .std.resid
## 1 0.01782772 274.2346 0.002467191  -1.474712
## 2 0.01782772 274.2279 0.002515370  -1.489042
## 3 0.01782772 274.1661 0.002961275  -1.615643
## 4 0.01782772 274.1129 0.003345132  -1.717167
## 5 0.01782772 274.1236 0.003268097  -1.697280
## 6 0.01782772 274.1074 0.003384381  -1.727212
harju %>%
  ggplot(aes(factor(month, levels = month.abb), price_unit_area_mean, group = year)) +
  geom_line(alpha = 0.3) +
  geom_vline(xintercept = ymd("2008-09-15"), linetype = 2) +
  facet_wrap(~ area, scales = "free_y") +
  labs(title = bquote(Seasonal~trend~price~per~m^2~of~residential~apartments),
       subtitle = "Harju county",
       x = "Month",
       y = bquote(Mean~price~per~unit~area~(eur/m^2)),
       caption = "Source: Estonian Land Board, transactions database.") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5)) +
  geom_line(data = predicted_pua, aes(month, .fitted, group = 1), 
              color = "red", 
              size = 2)

Residuals? Add also year to model to visualise residuals.

predicted_trans2 <- harju %>% 
  lm(transactions ~ month + year + area, data = .) %>% 
  augment
predicted_trans2
##     transactions month year      area   .fitted  .se.fit       .resid
## 1             65   Jan 2005  10-29,99  88.58743 9.129342  -23.5874267
## 2            155   Jan 2005  30-40,99 153.91327 9.129342    1.0867306
## 3            253   Jan 2005  41-54,99 245.34585 9.129342    7.6541463
## 4            230   Jan 2005  55-69,99 200.94698 9.129342   29.0530227
## 5            118   Jan 2005 70-249,99 175.78967 9.129342  -57.7896739
## 6             63   Feb 2005  10-29,99  99.50743 9.129342  -36.5074267
## 7            175   Feb 2005  30-40,99 164.83327 9.129342   10.1667306
## 8            257   Feb 2005  41-54,99 256.26585 9.129342    0.7341463
## 9            249   Feb 2005  55-69,99 211.86698 9.129342   37.1330227
## 10           174   Feb 2005 70-249,99 186.70967 9.129342  -12.7096739
## 11            88   Mar 2005  10-29,99 125.02743 9.129342  -37.0274267
## 12           220   Mar 2005  30-40,99 190.35327 9.129342   29.6467306
## 13           350   Mar 2005  41-54,99 281.78585 9.129342   68.2141463
## 14           350   Mar 2005  55-69,99 237.38698 9.129342  112.6130227
## 15           199   Mar 2005 70-249,99 212.22967 9.129342  -13.2296739
## 16           101   Apr 2005  10-29,99 120.92076 9.129342  -19.9207601
## 17           202   Apr 2005  30-40,99 186.24660 9.129342   15.7533972
## 18           360   Apr 2005  41-54,99 277.67919 9.129342   82.3208130
## 19           329   Apr 2005  55-69,99 233.28031 9.129342   95.7196894
## 20           200   Apr 2005 70-249,99 208.12301 9.129342   -8.1230072
## 21           107   May 2005  10-29,99 123.94743 9.129342  -16.9474267
## 22           247   May 2005  30-40,99 189.27327 9.129342   57.7267306
## 23           404   May 2005  41-54,99 280.70585 9.129342  123.2941463
## 24           398   May 2005  55-69,99 236.30698 9.129342  161.6930227
## 25           226   May 2005 70-249,99 211.14967 9.129342   14.8503261
## 26           103   Jun 2005  10-29,99 106.98743 9.129342   -3.9874267
## 27           251   Jun 2005  30-40,99 172.31327 9.129342   78.6867306
## 28           408   Jun 2005  41-54,99 263.74585 9.129342  144.2541463
## 29           417   Jun 2005  55-69,99 219.34698 9.129342  197.6530227
## 30           232   Jun 2005 70-249,99 194.18967 9.129342   37.8103261
## 31           109   Jul 2005  10-29,99 111.74743 9.129342   -2.7474267
## 32           242   Jul 2005  30-40,99 177.07327 9.129342   64.9267306
## 33           422   Jul 2005  41-54,99 268.50585 9.129342  153.4941463
## 34           380   Jul 2005  55-69,99 224.10698 9.129342  155.8930227
## 35           241   Jul 2005 70-249,99 198.94967 9.129342   42.0503261
## 36           179   Aug 2005  10-29,99 119.45409 9.129342   59.5459066
## 37           297   Aug 2005  30-40,99 184.77994 9.129342  112.2200639
## 38           492   Aug 2005  41-54,99 276.21252 9.129342  215.7874796
## 39           421   Aug 2005  55-69,99 231.81364 9.129342  189.1863560
## 40           265   Aug 2005 70-249,99 206.65634 9.129342   58.3436594
## 41           177   Sep 2005  10-29,99 124.25409 9.129342   52.7459066
## 42           302   Sep 2005  30-40,99 189.57994 9.129342  112.4200639
## 43           472   Sep 2005  41-54,99 281.01252 9.129342  190.9874796
## 44           443   Sep 2005  55-69,99 236.61364 9.129342  206.3863560
## 45           281   Sep 2005 70-249,99 211.45634 9.129342   69.5436594
## 46           184   Oct 2005  10-29,99 128.05409 9.129342   55.9459066
## 47           334   Oct 2005  30-40,99 193.37994 9.129342  140.6200639
## 48           512   Oct 2005  41-54,99 284.81252 9.129342  227.1874796
## 49           411   Oct 2005  55-69,99 240.41364 9.129342  170.5863560
## 50           310   Oct 2005 70-249,99 215.25634 9.129342   94.7436594
## 51           166   Nov 2005  10-29,99 128.31564 9.243226   37.6843561
## 52           278   Nov 2005  30-40,99 193.64149 9.243226   84.3585134
## 53           530   Nov 2005  41-54,99 285.07407 9.243226  244.9259292
## 54           461   Nov 2005  55-69,99 240.67519 9.243226  220.3248056
## 55           338   Nov 2005 70-249,99 215.51789 9.243226  122.4821090
## 56           152   Dec 2005  10-29,99 124.98707 9.243226   27.0129276
## 57           323   Dec 2005  30-40,99 190.31292 9.243226  132.6870849
## 58           471   Dec 2005  41-54,99 281.74550 9.243226  189.2545006
## 59           457   Dec 2005  55-69,99 237.34662 9.243226  219.6533770
## 60           339   Dec 2005 70-249,99 212.18932 9.243226  126.8106804
## 61           129   Jan 2006  10-29,99  84.21063 8.912216   44.7893733
## 62           234   Jan 2006  30-40,99 149.53647 8.912216   84.4635306
## 63           447   Jan 2006  41-54,99 240.96905 8.912216  206.0309463
## 64           350   Jan 2006  55-69,99 196.57018 8.912216  153.4298227
## 65           229   Jan 2006 70-249,99 171.41287 8.912216   57.5871261
## 66           102   Feb 2006  10-29,99  95.13063 8.912216    6.8693733
## 67           190   Feb 2006  30-40,99 160.45647 8.912216   29.5435306
## 68           327   Feb 2006  41-54,99 251.88905 8.912216   75.1109463
## 69           321   Feb 2006  55-69,99 207.49018 8.912216  113.5098227
## 70           269   Feb 2006 70-249,99 182.33287 8.912216   86.6671261
## 71           178   Mar 2006  10-29,99 120.65063 8.912216   57.3493733
## 72           225   Mar 2006  30-40,99 185.97647 8.912216   39.0235306
## 73           414   Mar 2006  41-54,99 277.40905 8.912216  136.5909463
## 74           331   Mar 2006  55-69,99 233.01018 8.912216   97.9898227
## 75           272   Mar 2006 70-249,99 207.85287 8.912216   64.1471261
## 76            93   Apr 2006  10-29,99 116.54396 8.912216  -23.5439600
## 77           191   Apr 2006  30-40,99 181.86980 8.912216    9.1301973
## 78           288   Apr 2006  41-54,99 273.30239 8.912216   14.6976130
## 79           287   Apr 2006  55-69,99 228.90351 8.912216   58.0964894
## 80           235   Apr 2006 70-249,99 203.74621 8.912216   31.2537928
## 81            99   May 2006  10-29,99 119.57063 8.912216  -20.5706267
## 82           204   May 2006  30-40,99 184.89647 8.912216   19.1035306
## 83           362   May 2006  41-54,99 276.32905 8.912216   85.6709463
## 84           285   May 2006  55-69,99 231.93018 8.912216   53.0698227
## 85           232   May 2006 70-249,99 206.77287 8.912216   25.2271261
## 86            85   Jun 2006  10-29,99 102.61063 8.912216  -17.6106267
## 87           165   Jun 2006  30-40,99 167.93647 8.912216   -2.9364694
## 88           365   Jun 2006  41-54,99 259.36905 8.912216  105.6309463
## 89           285   Jun 2006  55-69,99 214.97018 8.912216   70.0298227
## 90           271   Jun 2006 70-249,99 189.81287 8.912216   81.1871261
## 91            84   Jul 2006  10-29,99 107.37063 8.912216  -23.3706267
## 92           180   Jul 2006  30-40,99 172.69647 8.912216    7.3035306
## 93           310   Jul 2006  41-54,99 264.12905 8.912216   45.8709463
## 94           278   Jul 2006  55-69,99 219.73018 8.912216   58.2698227
## 95           218   Jul 2006 70-249,99 194.57287 8.912216   23.4271261
## 96           139   Aug 2006  10-29,99 115.07729 8.912216   23.9227066
## 97           248   Aug 2006  30-40,99 180.40314 8.912216   67.5968639
## 98           426   Aug 2006  41-54,99 271.83572 8.912216  154.1642797
## 99           316   Aug 2006  55-69,99 227.43684 8.912216   88.5631561
## 100          243   Aug 2006 70-249,99 202.27954 8.912216   40.7204595
## 101          115   Sep 2006  10-29,99 119.87729 8.912216   -4.8772934
## 102          257   Sep 2006  30-40,99 185.20314 8.912216   71.7968639
## 103          395   Sep 2006  41-54,99 276.63572 8.912216  118.3642797
## 104          343   Sep 2006  55-69,99 232.23684 8.912216  110.7631561
## 105          271   Sep 2006 70-249,99 207.07954 8.912216   63.9204595
## 106          121   Oct 2006  10-29,99 123.67729 8.912216   -2.6772934
## 107          274   Oct 2006  30-40,99 189.00314 8.912216   84.9968639
## 108          476   Oct 2006  41-54,99 280.43572 8.912216  195.5642797
## 109          421   Oct 2006  55-69,99 236.03684 8.912216  184.9631561
## 110          309   Oct 2006 70-249,99 210.87954 8.912216   98.1204595
## 111          138   Nov 2006  10-29,99 123.93884 9.043198   14.0611562
## 112          308   Nov 2006  30-40,99 189.26469 9.043198  118.7353135
## 113          478   Nov 2006  41-54,99 280.69727 9.043198  197.3027292
## 114          367   Nov 2006  55-69,99 236.29839 9.043198  130.7016056
## 115          315   Nov 2006 70-249,99 211.14109 9.043198  103.8589090
## 116          119   Dec 2006  10-29,99 120.61027 9.043198   -1.6102724
## 117          240   Dec 2006  30-40,99 185.93612 9.043198   54.0638849
## 118          429   Dec 2006  41-54,99 277.36870 9.043198  151.6313006
## 119          363   Dec 2006  55-69,99 232.96982 9.043198  130.0301770
## 120          315   Dec 2006 70-249,99 207.81252 9.043198  107.1874804
## 121           99   Jan 2007  10-29,99  79.83383 8.727362   19.1661733
## 122          216   Jan 2007  30-40,99 145.15967 8.727362   70.8403306
## 123          342   Jan 2007  41-54,99 236.59225 8.727362  105.4077464
## 124          270   Jan 2007  55-69,99 192.19338 8.727362   77.8066228
## 125          219   Jan 2007 70-249,99 167.03607 8.727362   51.9639261
## 126          107   Feb 2007  10-29,99  90.75383 8.727362   16.2461733
## 127          239   Feb 2007  30-40,99 156.07967 8.727362   82.9203306
## 128          377   Feb 2007  41-54,99 247.51225 8.727362  129.4877464
## 129          297   Feb 2007  55-69,99 203.11338 8.727362   93.8866228
## 130          238   Feb 2007 70-249,99 177.95607 8.727362   60.0439261
## 131          122   Mar 2007  10-29,99 116.27383 8.727362    5.7261733
## 132          233   Mar 2007  30-40,99 181.59967 8.727362   51.4003306
## 133          457   Mar 2007  41-54,99 273.03225 8.727362  183.9677464
## 134          361   Mar 2007  55-69,99 228.63338 8.727362  132.3666228
## 135          258   Mar 2007 70-249,99 203.47607 8.727362   54.5239261
## 136          121   Apr 2007  10-29,99 112.16716 8.727362    8.8328400
## 137          261   Apr 2007  30-40,99 177.49300 8.727362   83.5069973
## 138          420   Apr 2007  41-54,99 268.92559 8.727362  151.0744130
## 139          322   Apr 2007  55-69,99 224.52671 8.727362   97.4732894
## 140          240   Apr 2007 70-249,99 199.36941 8.727362   40.6305928
## 141          120   May 2007  10-29,99 115.19383 8.727362    4.8061733
## 142          237   May 2007  30-40,99 180.51967 8.727362   56.4803306
## 143          414   May 2007  41-54,99 271.95225 8.727362  142.0477464
## 144          337   May 2007  55-69,99 227.55338 8.727362  109.4466228
## 145          305   May 2007 70-249,99 202.39607 8.727362  102.6039261
## 146           90   Jun 2007  10-29,99  98.23383 8.727362   -8.2338267
## 147          189   Jun 2007  30-40,99 163.55967 8.727362   25.4403306
## 148          312   Jun 2007  41-54,99 254.99225 8.727362   57.0077464
## 149          243   Jun 2007  55-69,99 210.59338 8.727362   32.4066228
## 150          205   Jun 2007 70-249,99 185.43607 8.727362   19.5639261
## 151           84   Jul 2007  10-29,99 102.99383 8.727362  -18.9938267
## 152          179   Jul 2007  30-40,99 168.31967 8.727362   10.6803306
## 153          304   Jul 2007  41-54,99 259.75225 8.727362   44.2477464
## 154          177   Jul 2007  55-69,99 215.35338 8.727362  -38.3533772
## 155          168   Jul 2007 70-249,99 190.19607 8.727362  -22.1960739
## 156          101   Aug 2007  10-29,99 110.70049 8.727362   -9.7004933
## 157          150   Aug 2007  30-40,99 176.02634 8.727362  -26.0263360
## 158          252   Aug 2007  41-54,99 267.45892 8.727362  -15.4589203
## 159          200   Aug 2007  55-69,99 223.06004 8.727362  -23.0600439
## 160          184   Aug 2007 70-249,99 197.90274 8.727362  -13.9027405
## 161           89   Sep 2007  10-29,99 115.50049 8.727362  -26.5004933
## 162          138   Sep 2007  30-40,99 180.82634 8.727362  -42.8263360
## 163          255   Sep 2007  41-54,99 272.25892 8.727362  -17.2589203
## 164          206   Sep 2007  55-69,99 227.86004 8.727362  -21.8600439
## 165          148   Sep 2007 70-249,99 202.70274 8.727362  -54.7027405
## 166           95   Oct 2007  10-29,99 119.30049 8.727362  -24.3004933
## 167          174   Oct 2007  30-40,99 184.62634 8.727362  -10.6263360
## 168          263   Oct 2007  41-54,99 276.05892 8.727362  -13.0589203
## 169          229   Oct 2007  55-69,99 231.66004 8.727362   -2.6600439
## 170          205   Oct 2007 70-249,99 206.50274 8.727362   -1.5027405
## 171           90   Nov 2007  10-29,99 119.56204 8.875706  -29.5620438
## 172          156   Nov 2007  30-40,99 184.88789 8.875706  -28.8878865
## 173          266   Nov 2007  41-54,99 276.32047 8.875706  -10.3204708
## 174          220   Nov 2007  55-69,99 231.92159 8.875706  -11.9215944
## 175          156   Nov 2007 70-249,99 206.76429 8.875706  -50.7642910
## 176           57   Dec 2007  10-29,99 116.23347 8.875706  -59.2334724
## 177          121   Dec 2007  30-40,99 181.55932 8.875706  -60.5593151
## 178          234   Dec 2007  41-54,99 272.99190 8.875706  -38.9918993
## 179          195   Dec 2007  55-69,99 228.59302 8.875706  -33.5930229
## 180          136   Dec 2007 70-249,99 203.43572 8.875706  -67.4357196
## 181           77   Jan 2008  10-29,99  75.45703 8.576865    1.5429734
## 182          118   Jan 2008  30-40,99 140.78287 8.576865  -22.7828693
## 183          194   Jan 2008  41-54,99 232.21545 8.576865  -38.2154536
## 184          158   Jan 2008  55-69,99 187.81658 8.576865  -29.8165772
## 185          116   Jan 2008 70-249,99 162.65927 8.576865  -46.6592738
## 186           64   Feb 2008  10-29,99  86.37703 8.576865  -22.3770266
## 187          134   Feb 2008  30-40,99 151.70287 8.576865  -17.7028693
## 188          237   Feb 2008  41-54,99 243.13545 8.576865   -6.1354536
## 189          181   Feb 2008  55-69,99 198.73658 8.576865  -17.7365772
## 190          158   Feb 2008 70-249,99 173.57927 8.576865  -15.5792738
## 191           70   Mar 2008  10-29,99 111.89703 8.576865  -41.8970266
## 192          112   Mar 2008  30-40,99 177.22287 8.576865  -65.2228693
## 193          236   Mar 2008  41-54,99 268.65545 8.576865  -32.6554536
## 194          214   Mar 2008  55-69,99 224.25658 8.576865  -10.2565772
## 195          181   Mar 2008 70-249,99 199.09927 8.576865  -18.0992738
## 196           82   Apr 2008  10-29,99 107.79036 8.576865  -25.7903600
## 197          166   Apr 2008  30-40,99 173.11620 8.576865   -7.1162027
## 198          239   Apr 2008  41-54,99 264.54879 8.576865  -25.5487869
## 199          221   Apr 2008  55-69,99 220.14991 8.576865    0.8500895
## 200          193   Apr 2008 70-249,99 194.99261 8.576865   -1.9926072
## 201           54   May 2008  10-29,99 110.81703 8.576865  -56.8170266
## 202          140   May 2008  30-40,99 176.14287 8.576865  -36.1428693
## 203          223   May 2008  41-54,99 267.57545 8.576865  -44.5754536
## 204          218   May 2008  55-69,99 223.17658 8.576865   -5.1765772
## 205          150   May 2008 70-249,99 198.01927 8.576865  -48.0192738
## 206           77   Jun 2008  10-29,99  93.85703 8.576865  -16.8570266
## 207          108   Jun 2008  30-40,99 159.18287 8.576865  -51.1828693
## 208          190   Jun 2008  41-54,99 250.61545 8.576865  -60.6154536
## 209          143   Jun 2008  55-69,99 206.21658 8.576865  -63.2165772
## 210          163   Jun 2008 70-249,99 181.05927 8.576865  -18.0592738
## 211           56   Jul 2008  10-29,99  98.61703 8.576865  -42.6170266
## 212          152   Jul 2008  30-40,99 163.94287 8.576865  -11.9428693
## 213          209   Jul 2008  41-54,99 255.37545 8.576865  -46.3754536
## 214          177   Jul 2008  55-69,99 210.97658 8.576865  -33.9765772
## 215          152   Jul 2008 70-249,99 185.81927 8.576865  -33.8192738
## 216           76   Aug 2008  10-29,99 106.32369 8.576865  -30.3236933
## 217           94   Aug 2008  30-40,99 171.64954 8.576865  -77.6495360
## 218          174   Aug 2008  41-54,99 263.08212 8.576865  -89.0821203
## 219          161   Aug 2008  55-69,99 218.68324 8.576865  -57.6832439
## 220          110   Aug 2008 70-249,99 193.52594 8.576865  -83.5259405
## 221           75   Sep 2008  10-29,99 111.12369 8.576865  -36.1236933
## 222          101   Sep 2008  30-40,99 176.44954 8.576865  -75.4495360
## 223          205   Sep 2008  41-54,99 267.88212 8.576865  -62.8821203
## 224          151   Sep 2008  55-69,99 223.48324 8.576865  -72.4832439
## 225          150   Sep 2008 70-249,99 198.32594 8.576865  -48.3259405
## 226           69   Oct 2008  10-29,99 114.92369 8.576865  -45.9236933
## 227          109   Oct 2008  30-40,99 180.24954 8.576865  -71.2495360
## 228          188   Oct 2008  41-54,99 271.68212 8.576865  -83.6821203
## 229          154   Oct 2008  55-69,99 227.28324 8.576865  -73.2832439
## 230          148   Oct 2008 70-249,99 202.12594 8.576865  -54.1259405
## 231           42   Nov 2008  10-29,99 115.18524 8.742620  -73.1852438
## 232           94   Nov 2008  30-40,99 180.51109 8.742620  -86.5110865
## 233          113   Nov 2008  41-54,99 271.94367 8.742620 -158.9436707
## 234          125   Nov 2008  55-69,99 227.54479 8.742620 -102.5447943
## 235          100   Nov 2008 70-249,99 202.38749 8.742620 -102.3874909
## 236           49   Dec 2008  10-29,99 111.85667 8.742620  -62.8566723
## 237           67   Dec 2008  30-40,99 177.18252 8.742620 -110.1825150
## 238          140   Dec 2008  41-54,99 268.61510 8.742620 -128.6150993
## 239          100   Dec 2008  55-69,99 224.21622 8.742620 -124.2162229
## 240          113   Dec 2008 70-249,99 199.05892 8.742620  -86.0589195
## 241           23   Jan 2009  10-29,99  71.08023 8.462559  -48.0802266
## 242           64   Jan 2009  30-40,99 136.40607 8.462559  -72.4060693
## 243           80   Jan 2009  41-54,99 227.83865 8.462559 -147.8386536
## 244           68   Jan 2009  55-69,99 183.43978 8.462559 -115.4397772
## 245           88   Jan 2009 70-249,99 158.28247 8.462559  -70.2824738
## 246           49   Feb 2009  10-29,99  82.00023 8.462559  -33.0002266
## 247           60   Feb 2009  30-40,99 147.32607 8.462559  -87.3260693
## 248           85   Feb 2009  41-54,99 238.75865 8.462559 -153.7586536
## 249           89   Feb 2009  55-69,99 194.35978 8.462559 -105.3597772
## 250           82   Feb 2009 70-249,99 169.20247 8.462559  -87.2024738
## 251           56   Mar 2009  10-29,99 107.52023 8.462559  -51.5202266
## 252           58   Mar 2009  30-40,99 172.84607 8.462559 -114.8460693
## 253           95   Mar 2009  41-54,99 264.27865 8.462559 -169.2786536
## 254           89   Mar 2009  55-69,99 219.87978 8.462559 -130.8797772
## 255           79   Mar 2009 70-249,99 194.72247 8.462559 -115.7224738
## 256           30   Apr 2009  10-29,99 103.41356 8.462559  -73.4135599
## 257           83   Apr 2009  30-40,99 168.73940 8.462559  -85.7394026
## 258          112   Apr 2009  41-54,99 260.17199 8.462559 -148.1719869
## 259          146   Apr 2009  55-69,99 215.77311 8.462559  -69.7731105
## 260          112   Apr 2009 70-249,99 190.61581 8.462559  -78.6158071
## 261           36   May 2009  10-29,99 106.44023 8.462559  -70.4402266
## 262           79   May 2009  30-40,99 171.76607 8.462559  -92.7660693
## 263          104   May 2009  41-54,99 263.19865 8.462559 -159.1986536
## 264           76   May 2009  55-69,99 218.79978 8.462559 -142.7997772
## 265           99   May 2009 70-249,99 193.64247 8.462559  -94.6424738
## 266           48   Jun 2009  10-29,99  89.48023 8.462559  -41.4802266
## 267           82   Jun 2009  30-40,99 154.80607 8.462559  -72.8060693
## 268          100   Jun 2009  41-54,99 246.23865 8.462559 -146.2386536
## 269           97   Jun 2009  55-69,99 201.83978 8.462559 -104.8397772
## 270           97   Jun 2009 70-249,99 176.68247 8.462559  -79.6824738
## 271           79   Jul 2009  10-29,99  94.24023 8.462559  -15.2402266
## 272           92   Jul 2009  30-40,99 159.56607 8.462559  -67.5660693
## 273          171   Jul 2009  41-54,99 250.99865 8.462559  -79.9986536
## 274          134   Jul 2009  55-69,99 206.59978 8.462559  -72.5997772
## 275          101   Jul 2009 70-249,99 181.44247 8.462559  -80.4424738
## 276           56   Aug 2009  10-29,99 101.94689 8.462559  -45.9468933
## 277           74   Aug 2009  30-40,99 167.27274 8.462559  -93.2727360
## 278          117   Aug 2009  41-54,99 258.70532 8.462559 -141.7053202
## 279          121   Aug 2009  55-69,99 214.30644 8.462559  -93.3064438
## 280          100   Aug 2009 70-249,99 189.14914 8.462559  -89.1491405
## 281           62   Sep 2009  10-29,99 106.74689 8.462559  -44.7468933
## 282          124   Sep 2009  30-40,99 172.07274 8.462559  -48.0727360
## 283          158   Sep 2009  41-54,99 263.50532 8.462559 -105.5053202
## 284          133   Sep 2009  55-69,99 219.10644 8.462559  -86.1064438
## 285          107   Sep 2009 70-249,99 193.94914 8.462559  -86.9491405
## 286           71   Oct 2009  10-29,99 110.54689 8.462559  -39.5468933
## 287          114   Oct 2009  30-40,99 175.87274 8.462559  -61.8727360
## 288          169   Oct 2009  41-54,99 267.30532 8.462559  -98.3053202
## 289          169   Oct 2009  55-69,99 222.90644 8.462559  -53.9064438
## 290          123   Oct 2009 70-249,99 197.74914 8.462559  -74.7491405
## 291           68   Nov 2009  10-29,99 110.80844 8.645530  -42.8084437
## 292          114   Nov 2009  30-40,99 176.13429 8.645530  -62.1342864
## 293          175   Nov 2009  41-54,99 267.56687 8.645530  -92.5668707
## 294          113   Nov 2009  55-69,99 223.16799 8.645530 -110.1679943
## 295          153   Nov 2009 70-249,99 198.01069 8.645530  -45.0106909
## 296           69   Dec 2009  10-29,99 107.47987 8.645530  -38.4798723
## 297          118   Dec 2009  30-40,99 172.80571 8.645530  -54.8057150
## 298          159   Dec 2009  41-54,99 264.23830 8.645530 -105.2382993
## 299          139   Dec 2009  55-69,99 219.83942 8.645530  -80.8394229
## 300          120   Dec 2009 70-249,99 194.68212 8.645530  -74.6821195
## 301           41   Jan 2010  10-29,99  66.70343 8.385924  -25.7034266
## 302           72   Jan 2010  30-40,99 132.02927 8.385924  -60.0292693
## 303          120   Jan 2010  41-54,99 223.46185 8.385924 -103.4618535
## 304           98   Jan 2010  55-69,99 179.06298 8.385924  -81.0629771
## 305           99   Jan 2010 70-249,99 153.90567 8.385924  -54.9056738
## 306           56   Feb 2010  10-29,99  77.62343 8.385924  -21.6234266
## 307          111   Feb 2010  30-40,99 142.94927 8.385924  -31.9492693
## 308          125   Feb 2010  41-54,99 234.38185 8.385924 -109.3818535
## 309          113   Feb 2010  55-69,99 189.98298 8.385924  -76.9829771
## 310           94   Feb 2010 70-249,99 164.82567 8.385924  -70.8256738
## 311           92   Mar 2010  10-29,99 103.14343 8.385924  -11.1434266
## 312          126   Mar 2010  30-40,99 168.46927 8.385924  -42.4692693
## 313          160   Mar 2010  41-54,99 259.90185 8.385924  -99.9018535
## 314          133   Mar 2010  55-69,99 215.50298 8.385924  -82.5029771
## 315          106   Mar 2010 70-249,99 190.34567 8.385924  -84.3456738
## 316           84   Apr 2010  10-29,99  99.03676 8.385924  -15.0367599
## 317          158   Apr 2010  30-40,99 164.36260 8.385924   -6.3626026
## 318          154   Apr 2010  41-54,99 255.79519 8.385924 -101.7951869
## 319          160   Apr 2010  55-69,99 211.39631 8.385924  -51.3963105
## 320          102   Apr 2010 70-249,99 186.23901 8.385924  -84.2390071
## 321           63   May 2010  10-29,99 102.06343 8.385924  -39.0634266
## 322          157   May 2010  30-40,99 167.38927 8.385924  -10.3892693
## 323          163   May 2010  41-54,99 258.82185 8.385924  -95.8218535
## 324          150   May 2010  55-69,99 214.42298 8.385924  -64.4229771
## 325          124   May 2010 70-249,99 189.26567 8.385924  -65.2656738
## 326           56   Jun 2010  10-29,99  85.10343 8.385924  -29.1034266
## 327          124   Jun 2010  30-40,99 150.42927 8.385924  -26.4292693
## 328          159   Jun 2010  41-54,99 241.86185 8.385924  -82.8618535
## 329          122   Jun 2010  55-69,99 197.46298 8.385924  -75.4629771
## 330          115   Jun 2010 70-249,99 172.30567 8.385924  -57.3056738
## 331           66   Jul 2010  10-29,99  89.86343 8.385924  -23.8634266
## 332          116   Jul 2010  30-40,99 155.18927 8.385924  -39.1892693
## 333          136   Jul 2010  41-54,99 246.62185 8.385924 -110.6218535
## 334          158   Jul 2010  55-69,99 202.22298 8.385924  -44.2229771
## 335          102   Jul 2010 70-249,99 177.06567 8.385924  -75.0656738
## 336           64   Aug 2010  10-29,99  97.57009 8.385924  -33.5700932
## 337           92   Aug 2010  30-40,99 162.89594 8.385924  -70.8959359
## 338          138   Aug 2010  41-54,99 254.32852 8.385924 -116.3285202
## 339          135   Aug 2010  55-69,99 209.92964 8.385924  -74.9296438
## 340           91   Aug 2010 70-249,99 184.77234 8.385924  -93.7723404
## 341           76   Sep 2010  10-29,99 102.37009 8.385924  -26.3700932
## 342          121   Sep 2010  30-40,99 167.69594 8.385924  -46.6959359
## 343          179   Sep 2010  41-54,99 259.12852 8.385924  -80.1285202
## 344          143   Sep 2010  55-69,99 214.72964 8.385924  -71.7296438
## 345          122   Sep 2010 70-249,99 189.57234 8.385924  -67.5723404
## 346           72   Oct 2010  10-29,99 106.17009 8.385924  -34.1700932
## 347          122   Oct 2010  30-40,99 171.49594 8.385924  -49.4959359
## 348          153   Oct 2010  41-54,99 262.92852 8.385924 -109.9285202
## 349          118   Oct 2010  55-69,99 218.52964 8.385924 -100.5296438
## 350          124   Oct 2010 70-249,99 193.37234 8.385924  -69.3723404
## 351           93   Nov 2010  10-29,99 106.43164 8.585657  -13.4316437
## 352          130   Nov 2010  30-40,99 171.75749 8.585657  -41.7574864
## 353          211   Nov 2010  41-54,99 263.19007 8.585657  -52.1900707
## 354          149   Nov 2010  55-69,99 218.79119 8.585657  -69.7911943
## 355          138   Nov 2010 70-249,99 193.63389 8.585657  -55.6338909
## 356          113   Dec 2010  10-29,99 103.10307 8.585657    9.8969277
## 357          121   Dec 2010  30-40,99 168.42891 8.585657  -47.4289150
## 358          163   Dec 2010  41-54,99 259.86150 8.585657  -96.8614992
## 359          165   Dec 2010  55-69,99 215.46262 8.585657  -50.4626228
## 360          136   Dec 2010 70-249,99 190.30532 8.585657  -54.3053195
## 361           44   Jan 2011  10-29,99  62.32663 8.347999  -18.3266265
## 362           84   Jan 2011  30-40,99 127.65247 8.347999  -43.6524692
## 363          109   Jan 2011  41-54,99 219.08505 8.347999 -110.0850535
## 364           90   Jan 2011  55-69,99 174.68618 8.347999  -84.6861771
## 365           76   Jan 2011 70-249,99 149.52887 8.347999  -73.5288737
## 366           44   Feb 2011  10-29,99  73.24663 8.347999  -29.2466265
## 367           88   Feb 2011  30-40,99 138.57247 8.347999  -50.5724692
## 368          122   Feb 2011  41-54,99 230.00505 8.347999 -108.0050535
## 369           97   Feb 2011  55-69,99 185.60618 8.347999  -88.6061771
## 370          110   Feb 2011 70-249,99 160.44887 8.347999  -50.4488737
## 371           97   Mar 2011  10-29,99  98.76663 8.347999   -1.7666265
## 372          103   Mar 2011  30-40,99 164.09247 8.347999  -61.0924692
## 373          149   Mar 2011  41-54,99 255.52505 8.347999 -106.5250535
## 374          120   Mar 2011  55-69,99 211.12618 8.347999  -91.1261771
## 375          109   Mar 2011 70-249,99 185.96887 8.347999  -76.9688737
## 376           50   Apr 2011  10-29,99  94.65996 8.347999  -44.6599599
## 377          100   Apr 2011  30-40,99 159.98580 8.347999  -59.9858026
## 378          146   Apr 2011  41-54,99 251.41839 8.347999 -105.4183868
## 379          120   Apr 2011  55-69,99 207.01951 8.347999  -87.0195104
## 380          117   Apr 2011 70-249,99 181.86221 8.347999  -64.8622071
## 381           76   May 2011  10-29,99  97.68663 8.347999  -21.6866265
## 382          100   May 2011  30-40,99 163.01247 8.347999  -63.0124692
## 383          143   May 2011  41-54,99 254.44505 8.347999 -111.4450535
## 384          122   May 2011  55-69,99 210.04618 8.347999  -88.0461771
## 385          117   May 2011 70-249,99 184.88887 8.347999  -67.8888737
## 386           46   Jun 2011  10-29,99  80.72663 8.347999  -34.7266265
## 387          115   Jun 2011  30-40,99 146.05247 8.347999  -31.0524692
## 388          168   Jun 2011  41-54,99 237.48505 8.347999  -69.4850535
## 389          119   Jun 2011  55-69,99 193.08618 8.347999  -74.0861771
## 390          125   Jun 2011 70-249,99 167.92887 8.347999  -42.9288737
## 391           47   Jul 2011  10-29,99  85.48663 8.347999  -38.4866265
## 392           90   Jul 2011  30-40,99 150.81247 8.347999  -60.8124692
## 393          155   Jul 2011  41-54,99 242.24505 8.347999  -87.2450535
## 394          119   Jul 2011  55-69,99 197.84618 8.347999  -78.8461771
## 395           95   Jul 2011 70-249,99 172.68887 8.347999  -77.6888737
## 396           69   Aug 2011  10-29,99  93.19329 8.347999  -24.1932932
## 397          131   Aug 2011  30-40,99 158.51914 8.347999  -27.5191359
## 398          196   Aug 2011  41-54,99 249.95172 8.347999  -53.9517202
## 399          133   Aug 2011  55-69,99 205.55284 8.347999  -72.5528438
## 400          127   Aug 2011 70-249,99 180.39554 8.347999  -53.3955404
## 401           65   Sep 2011  10-29,99  97.99329 8.347999  -32.9932932
## 402          125   Sep 2011  30-40,99 163.31914 8.347999  -38.3191359
## 403          153   Sep 2011  41-54,99 254.75172 8.347999 -101.7517202
## 404          136   Sep 2011  55-69,99 210.35284 8.347999  -74.3528438
## 405          158   Sep 2011 70-249,99 185.19554 8.347999  -27.1955404
## 406           78   Oct 2011  10-29,99 101.79329 8.347999  -23.7932932
## 407          131   Oct 2011  30-40,99 167.11914 8.347999  -36.1191359
## 408          180   Oct 2011  41-54,99 258.55172 8.347999  -78.5517202
## 409          124   Oct 2011  55-69,99 214.15284 8.347999  -90.1528438
## 410          129   Oct 2011 70-249,99 188.99554 8.347999  -59.9955404
## 411           58   Nov 2011  10-29,99 102.05484 8.563781  -44.0548437
## 412          114   Nov 2011  30-40,99 167.38069 8.563781  -53.3806864
## 413          178   Nov 2011  41-54,99 258.81327 8.563781  -80.8132706
## 414          174   Nov 2011  55-69,99 214.41439 8.563781  -40.4143942
## 415          130   Nov 2011 70-249,99 189.25709 8.563781  -59.2570909
## 416           82   Dec 2011  10-29,99  98.72627 8.563781  -16.7262722
## 417          138   Dec 2011  30-40,99 164.05211 8.563781  -26.0521149
## 418          204   Dec 2011  41-54,99 255.48470 8.563781  -51.4846992
## 419          153   Dec 2011  55-69,99 211.08582 8.563781  -58.0858228
## 420          135   Dec 2011 70-249,99 185.92852 8.563781  -50.9285194
## 421           72   Jan 2012  10-29,99  57.94983 8.349309   14.0501735
## 422          119   Jan 2012  30-40,99 123.27567 8.349309   -4.2756692
## 423          156   Jan 2012  41-54,99 214.70825 8.349309  -58.7082535
## 424          122   Jan 2012  55-69,99 170.30938 8.349309  -48.3093771
## 425           95   Jan 2012 70-249,99 145.15207 8.349309  -50.1520737
## 426           66   Feb 2012  10-29,99  68.86983 8.349309   -2.8698265
## 427           98   Feb 2012  30-40,99 134.19567 8.349309  -36.1956692
## 428          184   Feb 2012  41-54,99 225.62825 8.349309  -41.6282535
## 429          133   Feb 2012  55-69,99 181.22938 8.349309  -48.2293771
## 430          128   Feb 2012 70-249,99 156.07207 8.349309  -28.0720737
## 431           66   Mar 2012  10-29,99  94.38983 8.349309  -28.3898265
## 432          122   Mar 2012  30-40,99 159.71567 8.349309  -37.7156692
## 433          182   Mar 2012  41-54,99 251.14825 8.349309  -69.1482535
## 434          141   Mar 2012  55-69,99 206.74938 8.349309  -65.7493771
## 435          143   Mar 2012 70-249,99 181.59207 8.349309  -38.5920737
## 436           76   Apr 2012  10-29,99  90.28316 8.349309  -14.2831598
## 437          148   Apr 2012  30-40,99 155.60900 8.349309   -7.6090025
## 438          182   Apr 2012  41-54,99 247.04159 8.349309  -65.0415868
## 439          143   Apr 2012  55-69,99 202.64271 8.349309  -59.6427104
## 440          121   Apr 2012 70-249,99 177.48541 8.349309  -56.4854070
## 441           77   May 2012  10-29,99  93.30983 8.349309  -16.3098265
## 442          127   May 2012  30-40,99 158.63567 8.349309  -31.6356692
## 443          222   May 2012  41-54,99 250.06825 8.349309  -28.0682535
## 444          187   May 2012  55-69,99 205.66938 8.349309  -18.6693771
## 445          137   May 2012 70-249,99 180.51207 8.349309  -43.5120737
## 446           77   Jun 2012  10-29,99  76.34983 8.349309    0.6501735
## 447          118   Jun 2012  30-40,99 141.67567 8.349309  -23.6756692
## 448          204   Jun 2012  41-54,99 233.10825 8.349309  -29.1082535
## 449          141   Jun 2012  55-69,99 188.70938 8.349309  -47.7093771
## 450          147   Jun 2012 70-249,99 163.55207 8.349309  -16.5520737
## 451           86   Jul 2012  10-29,99  81.10983 8.349309    4.8901735
## 452          150   Jul 2012  30-40,99 146.43567 8.349309    3.5643308
## 453          180   Jul 2012  41-54,99 237.86825 8.349309  -57.8682535
## 454          145   Jul 2012  55-69,99 193.46938 8.349309  -48.4693771
## 455          136   Jul 2012 70-249,99 168.31207 8.349309  -32.3120737
## 456          100   Aug 2012  10-29,99  88.81649 8.349309   11.1835068
## 457          149   Aug 2012  30-40,99 154.14234 8.349309   -5.1423359
## 458          213   Aug 2012  41-54,99 245.57492 8.349309  -32.5749201
## 459          170   Aug 2012  55-69,99 201.17604 8.349309  -31.1760437
## 460          165   Aug 2012 70-249,99 176.01874 8.349309  -11.0187404
## 461           89   Sep 2012  10-29,99  93.61649 8.349309   -4.6164932
## 462          145   Sep 2012  30-40,99 158.94234 8.349309  -13.9423359
## 463          233   Sep 2012  41-54,99 250.37492 8.349309  -17.3749201
## 464          163   Sep 2012  55-69,99 205.97604 8.349309  -42.9760437
## 465          147   Sep 2012 70-249,99 180.81874 8.349309  -33.8187404
## 466           96   Oct 2012  10-29,99  97.41649 8.349309   -1.4164932
## 467          150   Oct 2012  30-40,99 162.74234 8.349309  -12.7423359
## 468          230   Oct 2012  41-54,99 254.17492 8.349309  -24.1749201
## 469          186   Oct 2012  55-69,99 209.77604 8.349309  -23.7760437
## 470          146   Oct 2012 70-249,99 184.61874 8.349309  -38.6187404
## 471          100   Nov 2012  10-29,99  97.67804 8.580193    2.3219564
## 472          152   Nov 2012  30-40,99 163.00389 8.580193  -11.0038863
## 473          242   Nov 2012  41-54,99 254.43647 8.580193  -12.4364706
## 474          191   Nov 2012  55-69,99 210.03759 8.580193  -19.0375942
## 475          156   Nov 2012 70-249,99 184.88029 8.580193  -28.8802908
## 476           68   Dec 2012  10-29,99  94.34947 8.580193  -26.3494722
## 477          123   Dec 2012  30-40,99 159.67531 8.580193  -36.6753149
## 478          150   Dec 2012  41-54,99 251.10790 8.580193 -101.1078992
## 479          131   Dec 2012  55-69,99 206.70902 8.580193  -75.7090228
## 480          124   Dec 2012 70-249,99 181.55172 8.580193  -57.5517194
## 481           86   Jan 2013  10-29,99  53.57303 8.389838   32.4269735
## 482          132   Jan 2013  30-40,99 118.89887 8.389838   13.1011308
## 483          169   Jan 2013  41-54,99 210.33145 8.389838  -41.3314534
## 484          155   Jan 2013  55-69,99 165.93258 8.389838  -10.9325770
## 485          117   Jan 2013 70-249,99 140.77527 8.389838  -23.7752737
## 486           79   Feb 2013  10-29,99  64.49303 8.389838   14.5069735
## 487          136   Feb 2013  30-40,99 129.81887 8.389838    6.1811308
## 488          202   Feb 2013  41-54,99 221.25145 8.389838  -19.2514534
## 489          165   Feb 2013  55-69,99 176.85258 8.389838  -11.8525770
## 490          145   Feb 2013 70-249,99 151.69527 8.389838   -6.6952737
## 491           73   Mar 2013  10-29,99  90.01303 8.389838  -17.0130265
## 492          120   Mar 2013  30-40,99 155.33887 8.389838  -35.3388692
## 493          180   Mar 2013  41-54,99 246.77145 8.389838  -66.7714534
## 494          172   Mar 2013  55-69,99 202.37258 8.389838  -30.3725770
## 495          154   Mar 2013 70-249,99 177.21527 8.389838  -23.2152737
## 496          109   Apr 2013  10-29,99  85.90636 8.389838   23.0936402
## 497          142   Apr 2013  30-40,99 151.23220 8.389838   -9.2322025
## 498          279   Apr 2013  41-54,99 242.66479 8.389838   36.3352132
## 499          188   Apr 2013  55-69,99 198.26591 8.389838  -10.2659104
## 500          148   Apr 2013 70-249,99 173.10861 8.389838  -25.1086070
## 501           94   May 2013  10-29,99  88.93303 8.389838    5.0669735
## 502          160   May 2013  30-40,99 154.25887 8.389838    5.7411308
## 503          245   May 2013  41-54,99 245.69145 8.389838   -0.6914534
## 504          191   May 2013  55-69,99 201.29258 8.389838  -10.2925770
## 505          175   May 2013 70-249,99 176.13527 8.389838   -1.1352737
## 506          109   Jun 2013  10-29,99  71.97303 8.389838   37.0269735
## 507          118   Jun 2013  30-40,99 137.29887 8.389838  -19.2988692
## 508          182   Jun 2013  41-54,99 228.73145 8.389838  -46.7314534
## 509          136   Jun 2013  55-69,99 184.33258 8.389838  -48.3325770
## 510          173   Jun 2013 70-249,99 159.17527 8.389838   13.8247263
## 511          104   Jul 2013  10-29,99  76.73303 8.389838   27.2669735
## 512          156   Jul 2013  30-40,99 142.05887 8.389838   13.9411308
## 513          228   Jul 2013  41-54,99 233.49145 8.389838   -5.4914534
## 514          179   Jul 2013  55-69,99 189.09258 8.389838  -10.0925770
## 515          162   Jul 2013 70-249,99 163.93527 8.389838   -1.9352737
## 516           87   Aug 2013  10-29,99  84.43969 8.389838    2.5603069
## 517          145   Aug 2013  30-40,99 149.76554 8.389838   -4.7655358
## 518          232   Aug 2013  41-54,99 241.19812 8.389838   -9.1981201
## 519          188   Aug 2013  55-69,99 196.79924 8.389838   -8.7992437
## 520          153   Aug 2013 70-249,99 171.64194 8.389838  -18.6419403
## 521          122   Sep 2013  10-29,99  89.23969 8.389838   32.7603069
## 522          160   Sep 2013  30-40,99 154.56554 8.389838    5.4344642
## 523          206   Sep 2013  41-54,99 245.99812 8.389838  -39.9981201
## 524          192   Sep 2013  55-69,99 201.59924 8.389838   -9.5992437
## 525          154   Sep 2013 70-249,99 176.44194 8.389838  -22.4419403
## 526          106   Oct 2013  10-29,99  93.03969 8.389838   12.9603069
## 527          162   Oct 2013  30-40,99 158.36554 8.389838    3.6344642
## 528          278   Oct 2013  41-54,99 249.79812 8.389838   28.2018799
## 529          228   Oct 2013  55-69,99 205.39924 8.389838   22.6007563
## 530          163   Oct 2013 70-249,99 180.24194 8.389838  -17.2419403
## 531           88   Nov 2013  10-29,99  93.30124 8.634675   -5.3012436
## 532          170   Nov 2013  30-40,99 158.62709 8.634675   11.3729137
## 533          256   Nov 2013  41-54,99 250.05967 8.634675    5.9403294
## 534          208   Nov 2013  55-69,99 205.66079 8.634675    2.3392058
## 535          128   Nov 2013 70-249,99 180.50349 8.634675  -52.5034908
## 536           94   Dec 2013  10-29,99  89.97267 8.634675    4.0273278
## 537          141   Dec 2013  30-40,99 155.29851 8.634675  -14.2985149
## 538          196   Dec 2013  41-54,99 246.73110 8.634675  -50.7310991
## 539          164   Dec 2013  55-69,99 202.33222 8.634675  -38.3322227
## 540          165   Dec 2013 70-249,99 177.17492 8.634675  -12.1749194
## 541           91   Jan 2014  10-29,99  49.19623 8.469022   41.8037736
## 542          133   Jan 2014  30-40,99 114.52207 8.469022   18.4779309
## 543          235   Jan 2014  41-54,99 205.95465 8.469022   29.0453466
## 544          157   Jan 2014  55-69,99 161.55578 8.469022   -4.5557770
## 545          135   Jan 2014 70-249,99 136.39847 8.469022   -1.3984736
## 546           72   Feb 2014  10-29,99  60.11623 8.469022   11.8837736
## 547          127   Feb 2014  30-40,99 125.44207 8.469022    1.5579309
## 548          222   Feb 2014  41-54,99 216.87465 8.469022    5.1253466
## 549          169   Feb 2014  55-69,99 172.47578 8.469022   -3.4757770
## 550          162   Feb 2014 70-249,99 147.31847 8.469022   14.6815264
## 551           83   Mar 2014  10-29,99  85.63623 8.469022   -2.6362264
## 552          157   Mar 2014  30-40,99 150.96207 8.469022    6.0379309
## 553          253   Mar 2014  41-54,99 242.39465 8.469022   10.6053466
## 554          176   Mar 2014  55-69,99 197.99578 8.469022  -21.9957770
## 555          177   Mar 2014 70-249,99 172.83847 8.469022    4.1615264
## 556          127   Apr 2014  10-29,99  81.52956 8.469022   45.4704402
## 557          158   Apr 2014  30-40,99 146.85540 8.469022   11.1445975
## 558          199   Apr 2014  41-54,99 238.28799 8.469022  -39.2879867
## 559          183   Apr 2014  55-69,99 193.88911 8.469022  -10.8891103
## 560          180   Apr 2014 70-249,99 168.73181 8.469022   11.2681930
## 561          109   May 2014  10-29,99  84.55623 8.469022   24.4437736
## 562          137   May 2014  30-40,99 149.88207 8.469022  -12.8820691
## 563          206   May 2014  41-54,99 241.31465 8.469022  -35.3146534
## 564          152   May 2014  55-69,99 196.91578 8.469022  -44.9157770
## 565          158   May 2014 70-249,99 171.75847 8.469022  -13.7584736
## 566          107   Jun 2014  10-29,99  67.59623 8.469022   39.4037736
## 567          122   Jun 2014  30-40,99 132.92207 8.469022  -10.9220691
## 568          176   Jun 2014  41-54,99 224.35465 8.469022  -48.3546534
## 569          140   Jun 2014  55-69,99 179.95578 8.469022  -39.9557770
## 570          162   Jun 2014 70-249,99 154.79847 8.469022    7.2015264
## 571          104   Jul 2014  10-29,99  72.35623 8.469022   31.6437736
## 572          129   Jul 2014  30-40,99 137.68207 8.469022   -8.6820691
## 573          209   Jul 2014  41-54,99 229.11465 8.469022  -20.1146534
## 574          162   Jul 2014  55-69,99 184.71578 8.469022  -22.7157770
## 575          189   Jul 2014 70-249,99 159.55847 8.469022   29.4415264
## 576           80   Aug 2014  10-29,99  80.06289 8.469022   -0.0628931
## 577          130   Aug 2014  30-40,99 145.38874 8.469022  -15.3887358
## 578          190   Aug 2014  41-54,99 236.82132 8.469022  -46.8213201
## 579          165   Aug 2014  55-69,99 192.42244 8.469022  -27.4224437
## 580          151   Aug 2014 70-249,99 167.26514 8.469022  -16.2651403
## 581          100   Sep 2014  10-29,99  84.86289 8.469022   15.1371069
## 582          154   Sep 2014  30-40,99 150.18874 8.469022    3.8112642
## 583          268   Sep 2014  41-54,99 241.62132 8.469022   26.3786799
## 584          196   Sep 2014  55-69,99 197.22244 8.469022   -1.2224437
## 585          183   Sep 2014 70-249,99 172.06514 8.469022   10.9348597
## 586           85   Oct 2014  10-29,99  88.66289 8.469022   -3.6628931
## 587          179   Oct 2014  30-40,99 153.98874 8.469022   25.0112642
## 588          224   Oct 2014  41-54,99 245.42132 8.469022  -21.4213201
## 589          228   Oct 2014  55-69,99 201.02244 8.469022   26.9775563
## 590          210   Oct 2014 70-249,99 175.86514 8.469022   34.1348597
## 591          108   Nov 2014  10-29,99  88.92444 8.726513   19.0755564
## 592          152   Nov 2014  30-40,99 154.25029 8.726513   -2.2502863
## 593          214   Nov 2014  41-54,99 245.68287 8.726513  -31.6828705
## 594          197   Nov 2014  55-69,99 201.28399 8.726513   -4.2839941
## 595          156   Nov 2014 70-249,99 176.12669 8.726513  -20.1266908
## 596           79   Dec 2014  10-29,99  85.59587 8.726513   -6.5958721
## 597          143   Dec 2014  30-40,99 150.92171 8.726513   -7.9217148
## 598          257   Dec 2014  41-54,99 242.35430 8.726513   14.6457009
## 599          202   Dec 2014  55-69,99 197.95542 8.726513    4.0445773
## 600          176   Dec 2014 70-249,99 172.79812 8.726513    3.2018807
## 601           91   Jan 2014  10-29,99  49.19623 8.469022   41.8037736
## 602          133   Jan 2014  30-40,99 114.52207 8.469022   18.4779309
## 603          235   Jan 2014  41-54,99 205.95465 8.469022   29.0453466
## 604          157   Jan 2014  55-69,99 161.55578 8.469022   -4.5557770
## 605          135   Jan 2014 70-249,99 136.39847 8.469022   -1.3984736
## 606           72   Feb 2014  10-29,99  60.11623 8.469022   11.8837736
## 607          127   Feb 2014  30-40,99 125.44207 8.469022    1.5579309
## 608          222   Feb 2014  41-54,99 216.87465 8.469022    5.1253466
## 609          169   Feb 2014  55-69,99 172.47578 8.469022   -3.4757770
## 610          162   Feb 2014 70-249,99 147.31847 8.469022   14.6815264
## 611           83   Mar 2014  10-29,99  85.63623 8.469022   -2.6362264
## 612          157   Mar 2014  30-40,99 150.96207 8.469022    6.0379309
## 613          253   Mar 2014  41-54,99 242.39465 8.469022   10.6053466
## 614          176   Mar 2014  55-69,99 197.99578 8.469022  -21.9957770
## 615          177   Mar 2014 70-249,99 172.83847 8.469022    4.1615264
## 616          127   Apr 2014  10-29,99  81.52956 8.469022   45.4704402
## 617          158   Apr 2014  30-40,99 146.85540 8.469022   11.1445975
## 618          199   Apr 2014  41-54,99 238.28799 8.469022  -39.2879867
## 619          183   Apr 2014  55-69,99 193.88911 8.469022  -10.8891103
## 620          180   Apr 2014 70-249,99 168.73181 8.469022   11.2681930
## 621          109   May 2014  10-29,99  84.55623 8.469022   24.4437736
## 622          137   May 2014  30-40,99 149.88207 8.469022  -12.8820691
## 623          206   May 2014  41-54,99 241.31465 8.469022  -35.3146534
## 624          152   May 2014  55-69,99 196.91578 8.469022  -44.9157770
## 625          158   May 2014 70-249,99 171.75847 8.469022  -13.7584736
## 626          107   Jun 2014  10-29,99  67.59623 8.469022   39.4037736
## 627          122   Jun 2014  30-40,99 132.92207 8.469022  -10.9220691
## 628          176   Jun 2014  41-54,99 224.35465 8.469022  -48.3546534
## 629          140   Jun 2014  55-69,99 179.95578 8.469022  -39.9557770
## 630          162   Jun 2014 70-249,99 154.79847 8.469022    7.2015264
## 631          104   Jul 2014  10-29,99  72.35623 8.469022   31.6437736
## 632          129   Jul 2014  30-40,99 137.68207 8.469022   -8.6820691
## 633          209   Jul 2014  41-54,99 229.11465 8.469022  -20.1146534
## 634          162   Jul 2014  55-69,99 184.71578 8.469022  -22.7157770
## 635          189   Jul 2014 70-249,99 159.55847 8.469022   29.4415264
## 636           80   Aug 2014  10-29,99  80.06289 8.469022   -0.0628931
## 637          130   Aug 2014  30-40,99 145.38874 8.469022  -15.3887358
## 638          190   Aug 2014  41-54,99 236.82132 8.469022  -46.8213201
## 639          165   Aug 2014  55-69,99 192.42244 8.469022  -27.4224437
## 640          151   Aug 2014 70-249,99 167.26514 8.469022  -16.2651403
## 641          100   Sep 2014  10-29,99  84.86289 8.469022   15.1371069
## 642          154   Sep 2014  30-40,99 150.18874 8.469022    3.8112642
## 643          268   Sep 2014  41-54,99 241.62132 8.469022   26.3786799
## 644          196   Sep 2014  55-69,99 197.22244 8.469022   -1.2224437
## 645          183   Sep 2014 70-249,99 172.06514 8.469022   10.9348597
## 646           85   Oct 2014  10-29,99  88.66289 8.469022   -3.6628931
## 647          179   Oct 2014  30-40,99 153.98874 8.469022   25.0112642
## 648          224   Oct 2014  41-54,99 245.42132 8.469022  -21.4213201
## 649          228   Oct 2014  55-69,99 201.02244 8.469022   26.9775563
## 650          210   Oct 2014 70-249,99 175.86514 8.469022   34.1348597
## 651          108   Nov 2014  10-29,99  88.92444 8.726513   19.0755564
## 652          152   Nov 2014  30-40,99 154.25029 8.726513   -2.2502863
## 653          214   Nov 2014  41-54,99 245.68287 8.726513  -31.6828705
## 654          197   Nov 2014  55-69,99 201.28399 8.726513   -4.2839941
## 655          156   Nov 2014 70-249,99 176.12669 8.726513  -20.1266908
## 656           79   Dec 2014  10-29,99  85.59587 8.726513   -6.5958721
## 657          143   Dec 2014  30-40,99 150.92171 8.726513   -7.9217148
## 658          257   Dec 2014  41-54,99 242.35430 8.726513   14.6457009
## 659          202   Dec 2014  55-69,99 197.95542 8.726513    4.0445773
## 660          176   Dec 2014 70-249,99 172.79812 8.726513    3.2018807
## 661           80   Jan 2015  10-29,99  44.81943 8.585790   35.1805736
## 662          131   Jan 2015  30-40,99 110.14527 8.585790   20.8547309
## 663          186   Jan 2015  41-54,99 201.57785 8.585790  -15.5778534
## 664          139   Jan 2015  55-69,99 157.17898 8.585790  -18.1789770
## 665          128   Jan 2015 70-249,99 132.02167 8.585790   -4.0216736
## 666           83   Feb 2015  10-29,99  55.73943 8.585790   27.2605736
## 667          137   Feb 2015  30-40,99 121.06527 8.585790   15.9347309
## 668          261   Feb 2015  41-54,99 212.49785 8.585790   48.5021466
## 669          181   Feb 2015  55-69,99 168.09898 8.585790   12.9010230
## 670          155   Feb 2015 70-249,99 142.94167 8.585790   12.0583264
## 671           92   Mar 2015  10-29,99  81.25943 8.585790   10.7405736
## 672          176   Mar 2015  30-40,99 146.58527 8.585790   29.4147309
## 673          268   Mar 2015  41-54,99 238.01785 8.585790   29.9821466
## 674          199   Mar 2015  55-69,99 193.61898 8.585790    5.3810230
## 675          210   Mar 2015 70-249,99 168.46167 8.585790   41.5383264
## 676          127   Apr 2015  10-29,99  77.15276 8.585790   49.8472403
## 677          175   Apr 2015  30-40,99 142.47860 8.585790   32.5213976
## 678          268   Apr 2015  41-54,99 233.91119 8.585790   34.0888133
## 679          211   Apr 2015  55-69,99 189.51231 8.585790   21.4876897
## 680          213   Apr 2015 70-249,99 164.35501 8.585790   48.6449931
## 681           87   May 2015  10-29,99  80.17943 8.585790    6.8205736
## 682          167   May 2015  30-40,99 145.50527 8.585790   21.4947309
## 683          265   May 2015  41-54,99 236.93785 8.585790   28.0621466
## 684          234   May 2015  55-69,99 192.53898 8.585790   41.4610230
## 685          227   May 2015 70-249,99 167.38167 8.585790   59.6183264
## 686          100   Jun 2015  10-29,99  63.21943 8.585790   36.7805736
## 687          139   Jun 2015  30-40,99 128.54527 8.585790   10.4547309
## 688          254   Jun 2015  41-54,99 219.97785 8.585790   34.0221466
## 689          172   Jun 2015  55-69,99 175.57898 8.585790   -3.5789770
## 690          196   Jun 2015 70-249,99 150.42167 8.585790   45.5783264
## 691          110   Jul 2015  10-29,99  67.97943 8.585790   42.0205736
## 692          192   Jul 2015  30-40,99 133.30527 8.585790   58.6947309
## 693          253   Jul 2015  41-54,99 224.73785 8.585790   28.2621466
## 694          195   Jul 2015  55-69,99 180.33898 8.585790   14.6610230
## 695          179   Jul 2015 70-249,99 155.18167 8.585790   23.8183264
## 696          111   Aug 2015  10-29,99  75.68609 8.585790   35.3139069
## 697          148   Aug 2015  30-40,99 141.01194 8.585790    6.9880642
## 698          277   Aug 2015  41-54,99 232.44452 8.585790   44.5554800
## 699          189   Aug 2015  55-69,99 188.04564 8.585790    0.9543564
## 700          172   Aug 2015 70-249,99 162.88834 8.585790    9.1116597
## 701          113   Sep 2015  10-29,99  80.48609 8.585790   32.5139069
## 702          141   Sep 2015  30-40,99 145.81194 8.585790   -4.8119358
## 703          249   Sep 2015  41-54,99 237.24452 8.585790   11.7554800
## 704          177   Sep 2015  55-69,99 192.84564 8.585790  -15.8456436
## 705          170   Sep 2015 70-249,99 167.68834 8.585790    2.3116597
## 706           79   Oct 2015  10-29,99  84.28609 8.585790   -5.2860931
## 707          208   Oct 2015  30-40,99 149.61194 8.585790   58.3880642
## 708          260   Oct 2015  41-54,99 241.04452 8.585790   18.9554800
## 709          222   Oct 2015  55-69,99 196.64564 8.585790   25.3543564
## 710          189   Oct 2015 70-249,99 171.48834 8.585790   17.5116597
## 711           79   Nov 2015  10-29,99  84.54764 8.854546   -5.5476435
## 712          184   Nov 2015  30-40,99 149.87349 8.854546   34.1265138
## 713          278   Nov 2015  41-54,99 241.30607 8.854546   36.6939295
## 714          209   Nov 2015  55-69,99 196.90719 8.854546   12.0928059
## 715          228   Nov 2015 70-249,99 171.74989 8.854546   56.2501093
## 716          107   Dec 2015  10-29,99  81.21907 8.854546   25.7809279
## 717          145   Dec 2015  30-40,99 146.54491 8.854546   -1.5449148
## 718          291   Dec 2015  41-54,99 237.97750 8.854546   53.0225009
## 719          238   Dec 2015  55-69,99 193.57862 8.854546   44.4213773
## 720          295   Dec 2015 70-249,99 168.42132 8.854546  126.5786807
## 721           80   Jan 2015  10-29,99  44.81943 8.585790   35.1805736
## 722          131   Jan 2015  30-40,99 110.14527 8.585790   20.8547309
## 723          186   Jan 2015  41-54,99 201.57785 8.585790  -15.5778534
## 724          139   Jan 2015  55-69,99 157.17898 8.585790  -18.1789770
## 725          128   Jan 2015 70-249,99 132.02167 8.585790   -4.0216736
## 726           83   Feb 2015  10-29,99  55.73943 8.585790   27.2605736
## 727          137   Feb 2015  30-40,99 121.06527 8.585790   15.9347309
## 728          261   Feb 2015  41-54,99 212.49785 8.585790   48.5021466
## 729          181   Feb 2015  55-69,99 168.09898 8.585790   12.9010230
## 730          155   Feb 2015 70-249,99 142.94167 8.585790   12.0583264
## 731           92   Mar 2015  10-29,99  81.25943 8.585790   10.7405736
## 732          176   Mar 2015  30-40,99 146.58527 8.585790   29.4147309
## 733          268   Mar 2015  41-54,99 238.01785 8.585790   29.9821466
## 734          199   Mar 2015  55-69,99 193.61898 8.585790    5.3810230
## 735          210   Mar 2015 70-249,99 168.46167 8.585790   41.5383264
## 736          127   Apr 2015  10-29,99  77.15276 8.585790   49.8472403
## 737          175   Apr 2015  30-40,99 142.47860 8.585790   32.5213976
## 738          268   Apr 2015  41-54,99 233.91119 8.585790   34.0888133
## 739          211   Apr 2015  55-69,99 189.51231 8.585790   21.4876897
## 740          213   Apr 2015 70-249,99 164.35501 8.585790   48.6449931
## 741           87   May 2015  10-29,99  80.17943 8.585790    6.8205736
## 742          167   May 2015  30-40,99 145.50527 8.585790   21.4947309
## 743          265   May 2015  41-54,99 236.93785 8.585790   28.0621466
## 744          234   May 2015  55-69,99 192.53898 8.585790   41.4610230
## 745          227   May 2015 70-249,99 167.38167 8.585790   59.6183264
## 746          100   Jun 2015  10-29,99  63.21943 8.585790   36.7805736
## 747          139   Jun 2015  30-40,99 128.54527 8.585790   10.4547309
## 748          254   Jun 2015  41-54,99 219.97785 8.585790   34.0221466
## 749          172   Jun 2015  55-69,99 175.57898 8.585790   -3.5789770
## 750          196   Jun 2015 70-249,99 150.42167 8.585790   45.5783264
## 751          110   Jul 2015  10-29,99  67.97943 8.585790   42.0205736
## 752          192   Jul 2015  30-40,99 133.30527 8.585790   58.6947309
## 753          253   Jul 2015  41-54,99 224.73785 8.585790   28.2621466
## 754          195   Jul 2015  55-69,99 180.33898 8.585790   14.6610230
## 755          179   Jul 2015 70-249,99 155.18167 8.585790   23.8183264
## 756          111   Aug 2015  10-29,99  75.68609 8.585790   35.3139069
## 757          148   Aug 2015  30-40,99 141.01194 8.585790    6.9880642
## 758          277   Aug 2015  41-54,99 232.44452 8.585790   44.5554800
## 759          189   Aug 2015  55-69,99 188.04564 8.585790    0.9543564
## 760          172   Aug 2015 70-249,99 162.88834 8.585790    9.1116597
## 761          113   Sep 2015  10-29,99  80.48609 8.585790   32.5139069
## 762          141   Sep 2015  30-40,99 145.81194 8.585790   -4.8119358
## 763          249   Sep 2015  41-54,99 237.24452 8.585790   11.7554800
## 764          177   Sep 2015  55-69,99 192.84564 8.585790  -15.8456436
## 765          170   Sep 2015 70-249,99 167.68834 8.585790    2.3116597
## 766           79   Oct 2015  10-29,99  84.28609 8.585790   -5.2860931
## 767          208   Oct 2015  30-40,99 149.61194 8.585790   58.3880642
## 768          260   Oct 2015  41-54,99 241.04452 8.585790   18.9554800
## 769          222   Oct 2015  55-69,99 196.64564 8.585790   25.3543564
## 770          189   Oct 2015 70-249,99 171.48834 8.585790   17.5116597
## 771           79   Nov 2015  10-29,99  84.54764 8.854546   -5.5476435
## 772          184   Nov 2015  30-40,99 149.87349 8.854546   34.1265138
## 773          278   Nov 2015  41-54,99 241.30607 8.854546   36.6939295
## 774          209   Nov 2015  55-69,99 196.90719 8.854546   12.0928059
## 775          228   Nov 2015 70-249,99 171.74989 8.854546   56.2501093
## 776          107   Dec 2015  10-29,99  81.21907 8.854546   25.7809279
## 777          145   Dec 2015  30-40,99 146.54491 8.854546   -1.5449148
## 778          291   Dec 2015  41-54,99 237.97750 8.854546   53.0225009
## 779          238   Dec 2015  55-69,99 193.57862 8.854546   44.4213773
## 780          295   Dec 2015 70-249,99 168.42132 8.854546  126.5786807
## 781           73   Jan 2016  10-29,99  40.44263 8.738638   32.5573736
## 782          118   Jan 2016  30-40,99 105.76847 8.738638   12.2315309
## 783          214   Jan 2016  41-54,99 197.20105 8.738638   16.7989467
## 784          146   Jan 2016  55-69,99 152.80218 8.738638   -6.8021769
## 785          133   Jan 2016 70-249,99 127.64487 8.738638    5.3551264
## 786           89   Feb 2016  10-29,99  51.36263 8.738638   37.6373736
## 787          128   Feb 2016  30-40,99 116.68847 8.738638   11.3115309
## 788          269   Feb 2016  41-54,99 208.12105 8.738638   60.8789467
## 789          210   Feb 2016  55-69,99 163.72218 8.738638   46.2778231
## 790          148   Feb 2016 70-249,99 138.56487 8.738638    9.4351264
## 791          102   Mar 2016  10-29,99  76.88263 8.738638   25.1173736
## 792          183   Mar 2016  30-40,99 142.20847 8.738638   40.7915309
## 793          276   Mar 2016  41-54,99 233.64105 8.738638   42.3589467
## 794          220   Mar 2016  55-69,99 189.24218 8.738638   30.7578231
## 795          205   Mar 2016 70-249,99 164.08487 8.738638   40.9151264
## 796           84   Apr 2016  10-29,99  72.77596 8.738638   11.2240403
## 797          190   Apr 2016  30-40,99 138.10180 8.738638   51.8981976
## 798          276   Apr 2016  41-54,99 229.53439 8.738638   46.4656133
## 799          171   Apr 2016  55-69,99 185.13551 8.738638  -14.1355103
## 800          209   Apr 2016 70-249,99 159.97821 8.738638   49.0217931
## 801           90   May 2016  10-29,99  75.80263 8.738638   14.1973736
## 802          172   May 2016  30-40,99 141.12847 8.738638   30.8715309
## 803          275   May 2016  41-54,99 232.56105 8.738638   42.4389467
## 804          209   May 2016  55-69,99 188.16218 8.738638   20.8378231
## 805          244   May 2016 70-249,99 163.00487 8.738638   80.9951264
## 806           79   Jun 2016  10-29,99  58.84263 8.738638   20.1573736
## 807          134   Jun 2016  30-40,99 124.16847 8.738638    9.8315309
## 808          231   Jun 2016  41-54,99 215.60105 8.738638   15.3989467
## 809          223   Jun 2016  55-69,99 171.20218 8.738638   51.7978231
## 810          229   Jun 2016 70-249,99 146.04487 8.738638   82.9551264
## 811           77   Jul 2016  10-29,99  63.60263 8.738638   13.3973736
## 812          166   Jul 2016  30-40,99 128.92847 8.738638   37.0715309
## 813          278   Jul 2016  41-54,99 220.36105 8.738638   57.6389467
## 814          174   Jul 2016  55-69,99 175.96218 8.738638   -1.9621769
## 815          198   Jul 2016 70-249,99 150.80487 8.738638   47.1951264
## 816           90   Aug 2016  10-29,99  71.30929 8.738638   18.6907070
## 817          177   Aug 2016  30-40,99 136.63514 8.738638   40.3648643
## 818          296   Aug 2016  41-54,99 228.06772 8.738638   67.9322800
## 819          240   Aug 2016  55-69,99 183.66884 8.738638   56.3311564
## 820          225   Aug 2016 70-249,99 158.51154 8.738638   66.4884598
## 821          104   Sep 2016  10-29,99  76.10929 8.738638   27.8907070
## 822          174   Sep 2016  30-40,99 141.43514 8.738638   32.5648643
## 823          288   Sep 2016  41-54,99 232.86772 8.738638   55.1322800
## 824          203   Sep 2016  55-69,99 188.46884 8.738638   14.5311564
## 825          189   Sep 2016 70-249,99 163.31154 8.738638   25.6884598
## 826           87   Oct 2016  10-29,99  79.90929 8.738638    7.0907070
## 827          154   Oct 2016  30-40,99 145.23514 8.738638    8.7648643
## 828          298   Oct 2016  41-54,99 236.66772 8.738638   61.3322800
## 829          222   Oct 2016  55-69,99 192.26884 8.738638   29.7311564
## 830          214   Oct 2016 70-249,99 167.11154 8.738638   46.8884598
## 831           70   Nov 2016  10-29,99  80.17084 9.017232  -10.1708435
## 832          164   Nov 2016  30-40,99 145.49669 9.017232   18.5033138
## 833          288   Nov 2016  41-54,99 236.92927 9.017232   51.0707295
## 834          252   Nov 2016  55-69,99 192.53039 9.017232   59.4696059
## 835          211   Nov 2016 70-249,99 167.37309 9.017232   43.6269093
## 836           87   Dec 2016  10-29,99  76.84227 9.017232   10.1577279
## 837          195   Dec 2016  30-40,99 142.16811 9.017232   52.8318852
## 838          296   Dec 2016  41-54,99 233.60070 9.017232   62.3993010
## 839          285   Dec 2016  55-69,99 189.20182 9.017232   95.7981774
## 840          272   Dec 2016 70-249,99 164.04452 9.017232  107.9554807
## 841           84   Jan 2017  10-29,99  36.06583 8.925712   47.9341737
## 842          152   Jan 2017  30-40,99 101.39167 8.925712   50.6083310
## 843          260   Jan 2017  41-54,99 192.82425 8.925712   67.1757467
## 844          211   Jan 2017  55-69,99 148.42538 8.925712   62.5746231
## 845          227   Jan 2017 70-249,99 123.26807 8.925712  103.7319265
## 846           70   Feb 2017  10-29,99  46.98583 8.925712   23.0141737
## 847          129   Feb 2017  30-40,99 112.31167 8.925712   16.6883310
## 848          221   Feb 2017  41-54,99 203.74425 8.925712   17.2557467
## 849          211   Feb 2017  55-69,99 159.34538 8.925712   51.6546231
## 850          232   Feb 2017 70-249,99 134.18807 8.925712   97.8119265
## 851          104   Mar 2017  10-29,99  72.50583 8.925712   31.4941737
## 852          201   Mar 2017  30-40,99 137.83167 8.925712   63.1683310
## 853          340   Mar 2017  41-54,99 229.26425 8.925712  110.7357467
## 854          312   Mar 2017  55-69,99 184.86538 8.925712  127.1346231
## 855          258   Mar 2017 70-249,99 159.70807 8.925712   98.2919265
## 856          103   Apr 2017  10-29,99  68.39916 8.925712   34.6008403
## 857          151   Apr 2017  30-40,99 133.72500 8.925712   17.2749976
## 858          267   Apr 2017  41-54,99 225.15759 8.925712   41.8424134
## 859          190   Apr 2017  55-69,99 180.75871 8.925712    9.2412898
## 860          187   Apr 2017 70-249,99 155.60141 8.925712   31.3985931
## 861          105   May 2017  10-29,99  71.42583 8.925712   33.5741737
## 862          174   May 2017  30-40,99 136.75167 8.925712   37.2483310
## 863          261   May 2017  41-54,99 228.18425 8.925712   32.8157467
## 864          242   May 2017  55-69,99 183.78538 8.925712   58.2146231
## 865          256   May 2017 70-249,99 158.62807 8.925712   97.3719265
## 866           97   Jun 2017  10-29,99  54.46583 8.925712   42.5341737
## 867          157   Jun 2017  30-40,99 119.79167 8.925712   37.2083310
## 868          259   Jun 2017  41-54,99 211.22425 8.925712   47.7757467
## 869          202   Jun 2017  55-69,99 166.82538 8.925712   35.1746231
## 870          199   Jun 2017 70-249,99 141.66807 8.925712   57.3319265
## 871           73   Jul 2017  10-29,99  59.22583 8.925712   13.7741737
## 872          155   Jul 2017  30-40,99 124.55167 8.925712   30.4483310
## 873          288   Jul 2017  41-54,99 215.98425 8.925712   72.0157467
## 874          203   Jul 2017  55-69,99 171.58538 8.925712   31.4146231
## 875          218   Jul 2017 70-249,99 146.42807 8.925712   71.5719265
## 876           91   Aug 2017  10-29,99  66.93249 8.925712   24.0675070
## 877          188   Aug 2017  30-40,99 132.25834 8.925712   55.7416643
## 878          354   Aug 2017  41-54,99 223.69092 8.925712  130.3090800
## 879          247   Aug 2017  55-69,99 179.29204 8.925712   67.7079564
## 880          253   Aug 2017 70-249,99 154.13474 8.925712   98.8652598
## 881           86   Sep 2017  10-29,99  71.73249 8.925712   14.2675070
## 882          155   Sep 2017  30-40,99 137.05834 8.925712   17.9416643
## 883          306   Sep 2017  41-54,99 228.49092 8.925712   77.5090800
## 884          230   Sep 2017  55-69,99 184.09204 8.925712   45.9079564
## 885          237   Sep 2017 70-249,99 158.93474 8.925712   78.0652598
## 886           48   Oct 2017  10-29,99  75.53249 8.925712  -27.5324930
## 887           63   Oct 2017  30-40,99 140.85834 8.925712  -77.8583357
## 888          108   Oct 2017  41-54,99 232.29092 8.925712 -124.2909200
## 889           98   Oct 2017  55-69,99 187.89204 8.925712  -89.8920436
## 890          138   Oct 2017 70-249,99 162.73474 8.925712  -24.7347402
##           .hat   .sigma      .cooksd  .std.resid
## 1   0.02134301 62.52077 1.867599e-04 -0.38155192
## 2   0.02134301 62.52597 3.964297e-07  0.01757903
## 3   0.02134301 62.52544 1.966600e-05  0.12381403
## 4   0.02134301 62.51808 2.833382e-04  0.46996380
## 5   0.02134301 62.49468 1.121045e-03 -0.93480995
## 6   0.02134301 62.51350 4.473885e-04 -0.59054678
## 7   0.02134301 62.52502 3.469645e-05  0.16445777
## 8   0.02134301 62.52598 1.809204e-07  0.01187560
## 9   0.02134301 62.51306 4.628529e-04  0.60066647
## 10  0.02134301 62.52447 5.422396e-05 -0.20559261
## 11  0.02134301 62.51314 4.602242e-04 -0.59895834
## 12  0.02134301 62.51775 2.950367e-04  0.47956766
## 13  0.02134301 62.48237 1.561965e-03  1.10343697
## 14  0.02134301 62.40704 4.256961e-03  1.82163641
## 15  0.02134301 62.52435 5.875173e-05 -0.21400416
## 16  0.02134301 62.52227 1.332092e-04 -0.32223966
## 17  0.02134301 62.52366 8.330496e-05  0.25482810
## 18  0.02134301 62.46245 2.274792e-03  1.33162744
## 19  0.02134301 62.44007 3.075565e-03  1.54836863
## 20  0.02134301 62.52537 2.214910e-05 -0.13139835
## 21  0.02134301 62.52329 9.641174e-05 -0.27414280
## 22  0.02134301 62.49475 1.118604e-03  0.93379178
## 23  0.02134301 62.38338 5.102786e-03  1.99441504
## 24  0.02134301 62.28052 8.776169e-03  2.61555805
## 25  0.02134301 62.52392 7.402772e-05  0.24021995
## 26  0.02134301 62.52584 5.337131e-06 -0.06450090
## 27  0.02134301 62.46794 2.078382e-03  1.27284225
## 28  0.02134301 62.33069 6.985203e-03  2.33346552
## 29  0.02134301 62.15883 1.311382e-02  3.19724962
## 30  0.02134301 62.51259 4.798917e-04  0.61162257
## 31  0.02134301 62.52591 2.533814e-06 -0.04444257
## 32  0.02134301 62.48647 1.415042e-03  1.05025950
## 33  0.02134301 62.30482 7.908717e-03  2.48293243
## 34  0.02134301 62.29784 8.157851e-03  2.52173683
## 35  0.02134301 62.50941 5.935552e-04  0.68020912
## 36  0.02134301 62.49275 1.190217e-03  0.96321890
## 37  0.02134301 62.40787 4.227304e-03  1.81527988
## 38  0.02134301 62.08812 1.563057e-02  3.49059391
## 39  0.02134301 62.18970 1.201440e-02  3.06029220
## 40  0.02134301 62.49408 1.142641e-03  0.94377126
## 41  0.02134301 62.49991 9.338991e-04  0.85322161
## 42  0.02134301 62.40745 4.242385e-03  1.81851510
## 43  0.02134301 62.18325 1.224425e-02  3.08942731
## 44  0.02134301 62.12556 1.429830e-02  3.33852065
## 45  0.02134301 62.48065 1.623445e-03  1.12494327
## 46  0.02134301 62.49665 1.050652e-03  0.90498504
## 47  0.02134301 62.34042 6.637690e-03  2.27468034
## 48  0.02134301 62.04045 1.732572e-02  3.67500113
## 49  0.02134301 62.25271 9.768120e-03  2.75941725
## 50  0.02134301 62.44182 3.013164e-03  1.53258030
## 51  0.02187882 62.51267 4.892023e-04  0.60975182
## 52  0.02187882 62.45923 2.451456e-03  1.36496313
## 53  0.02187882 61.96100 2.066502e-02  3.96302459
## 54  0.02187882 62.06920 1.672219e-02  3.56496605
## 55  0.02187882 62.38517 5.167870e-03  1.98182206
## 56  0.02187882 62.51914 2.513678e-04  0.43708274
## 57  0.02187882 62.36070 6.064899e-03  2.14694370
## 58  0.02187882 62.18927 1.233840e-02  3.06223290
## 59  0.02187882 62.07199 1.662042e-02  3.55410200
## 60  0.02187882 62.37503 5.539594e-03  2.05186052
## 61  0.02033987 62.50720 6.404349e-04  0.72414511
## 62  0.02033987 62.45917 2.277527e-03  1.36558849
## 63  0.02033987 62.12736 1.355158e-02  3.33106475
## 64  0.02033987 62.30523 7.515270e-03  2.48062091
## 65  0.02033987 62.49493 1.058707e-03  0.93105647
## 66  0.02033987 62.52554 1.506466e-05  0.11106257
## 67  0.02033987 62.51781 2.786441e-04  0.47765355
## 68  0.02033987 62.47315 1.801074e-03  1.21437789
## 69  0.02033987 62.40526 4.113314e-03  1.83520280
## 70  0.02033987 62.45563 2.397915e-03  1.40121576
## 71  0.02033987 62.49519 1.049983e-03  0.92721253
## 72  0.02033987 62.51173 4.861588e-04  0.63092419
## 73  0.02033987 62.35109 5.956194e-03  2.20837352
## 74  0.02033987 62.43604 3.065399e-03  1.58427872
## 75  0.02033987 62.48745 1.313649e-03  1.03711716
## 76  0.02033987 62.52080 1.769636e-04 -0.38065376
## 77  0.02033987 62.52521 2.661248e-05  0.14761510
## 78  0.02033987 62.52396 6.896339e-05  0.23762790
## 79  0.02033987 62.49438 1.077519e-03  0.93929175
## 80  0.02033987 62.51684 3.118390e-04  0.50530471
## 81  0.02033987 62.52202 1.350890e-04 -0.33258154
## 82  0.02033987 62.52257 1.165071e-04  0.30886184
## 83  0.02033987 62.45724 2.343107e-03  1.38510973
## 84  0.02033987 62.49962 8.991254e-04  0.85802167
## 85  0.02033987 62.52003 2.031705e-04  0.40786684
## 86  0.02033987 62.52308 9.900899e-05 -0.28472489
## 87  0.02033987 62.52590 2.752808e-06 -0.04747622
## 88  0.02033987 62.42145 3.562110e-03  1.70781879
## 89  0.02033987 62.48006 1.565637e-03  1.13222736
## 90  0.02033987 62.46425 2.104260e-03  1.31261628
## 91  0.02033987 62.52087 1.743676e-04 -0.37785135
## 92  0.02033987 62.52549 1.702906e-05  0.11808194
## 93  0.02033987 62.50629 6.717388e-04  0.74163176
## 94  0.02033987 62.49419 1.083958e-03  0.94209417
## 95  0.02033987 62.52085 1.752117e-04  0.37876482
## 96  0.02033987 62.52063 1.827030e-04  0.38677726
## 97  0.02033987 62.48320 1.458741e-03  1.09289179
## 98  0.02033987 62.30311 7.587392e-03  2.49249546
## 99  0.02033987 62.45252 2.503982e-03  1.43187037
## 100 0.02033987 62.51046 5.293590e-04  0.65835977
## 101 0.02033987 62.52576 7.594213e-06 -0.07885505
## 102 0.02033987 62.47771 1.645644e-03  1.16079651
## 103 0.02033987 62.39470 4.472664e-03  1.91368863
## 104 0.02033987 62.41104 3.916658e-03  1.79079527
## 105 0.02033987 62.48773 1.304382e-03  1.03345246
## 106 0.02033987 62.52592 2.288321e-06 -0.04328591
## 107 0.02033987 62.45832 2.306380e-03  1.37421131
## 108 0.02033987 62.16694 1.220967e-02  3.16184190
## 109 0.02033987 62.20491 1.092183e-02  2.99044517
## 110 0.02033987 62.43580 3.073577e-03  1.58639083
## 111 0.02094212 62.52413 6.506895e-05  0.22740771
## 112 0.02094212 62.39379 4.639718e-03  1.92027777
## 113 0.02094212 62.16029 1.281144e-02  3.19092976
## 114 0.02094212 62.36577 5.622036e-03  2.11380575
## 115 0.02094212 62.42487 3.549926e-03  1.67968525
## 116 0.02094212 62.52596 8.533564e-07 -0.02604255
## 117 0.02094212 62.49860 9.619362e-04  0.87436226
## 118 0.02094212 62.31025 7.566752e-03  2.45229669
## 119 0.02094212 62.36741 5.564422e-03  2.10294690
## 120 0.02094212 62.41828 3.781115e-03  1.73351744
## 121 0.01950485 62.52255 1.122665e-04  0.30974266
## 122 0.01950485 62.47903 1.533701e-03  1.14484368
## 123 0.01950485 62.42198 3.395662e-03  1.70348431
## 124 0.01950485 62.46934 1.850174e-03  1.25742524
## 125 0.01950485 62.50073 8.252459e-04  0.83978394
## 126 0.01950485 62.52352 8.066435e-05  0.26255282
## 127 0.01950485 62.46164 2.101365e-03  1.34006738
## 128 0.01950485 62.36897 5.124327e-03  2.09263884
## 129 0.01950485 62.44349 2.693934e-03  1.51729256
## 130 0.01950485 62.49226 1.101838e-03  0.97036404
## 131 0.01950485 62.52568 1.002094e-05  0.09254013
## 132 0.01950485 62.50127 8.074419e-04  0.83067573
## 133 0.01950485 62.20864 1.034339e-02  2.97308481
## 134 0.01950485 62.36190 5.354716e-03  2.13916408
## 135 0.01950485 62.49817 9.085602e-04  0.88115585
## 136 0.01950485 62.52526 2.384406e-05  0.14274667
## 137 0.01950485 62.46073 2.131205e-03  1.34954844
## 138 0.01950485 62.31215 6.975274e-03  2.44149886
## 139 0.01950485 62.43706 2.903693e-03  1.57525633
## 140 0.01950485 62.51054 5.045286e-04  0.65662705
## 141 0.01950485 62.52577 7.059571e-06  0.07767210
## 142 0.01950485 62.49614 9.749311e-04  0.91277312
## 143 0.01950485 62.33698 6.166634e-03  2.29561978
## 144 0.01950485 62.41385 3.660869e-03  1.76875620
## 145 0.01950485 62.42744 3.217417e-03  1.65817204
## 146 0.01950485 62.52535 2.071967e-05 -0.13306607
## 147 0.01950485 62.51993 1.977994e-04  0.41113870
## 148 0.01950485 62.49558 9.932240e-04  0.92129663
## 149 0.01950485 62.51616 3.209571e-04  0.52372027
## 150 0.01950485 62.52241 1.169746e-04  0.31617070
## 151 0.01950485 62.52261 1.102565e-04 -0.30695738
## 152 0.01950485 62.52492 3.486172e-05  0.17260378
## 153 0.01950485 62.50767 5.983589e-04  0.71508351
## 154 0.01950485 62.51223 4.495590e-04 -0.61982519
## 155 0.01950485 62.52138 1.505677e-04 -0.35870859
## 156 0.01950485 62.52511 2.875856e-05 -0.15676873
## 157 0.01950485 62.51965 2.070168e-04 -0.42060908
## 158 0.01950485 62.52375 7.303613e-05 -0.24983010
## 159 0.01950485 62.52101 1.625173e-04 -0.37267112
## 160 0.01950485 62.52418 5.907181e-05 -0.22468083
## 161 0.01950485 62.51942 2.146285e-04 -0.42827189
## 162 0.01950485 62.50883 5.605331e-04 -0.69211224
## 163 0.01950485 62.52320 9.103465e-05 -0.27891973
## 164 0.01950485 62.52152 1.460433e-04 -0.35327804
## 165 0.01950485 62.49799 9.145293e-04 -0.88404566
## 166 0.01950485 62.52046 1.804719e-04 -0.39271790
## 167 0.01950485 62.52493 3.451013e-05 -0.17173118
## 168 0.01950485 62.52439 5.211875e-05 -0.21104394
## 169 0.01950485 62.52592 2.162505e-06 -0.04298871
## 170 0.01950485 62.52596 6.901563e-07 -0.02428564
## 171 0.02017356 62.51781 2.766182e-04 -0.47791230
## 172 0.02017356 62.51817 2.641456e-04 -0.46701360
## 173 0.02017356 62.52499 3.371405e-05 -0.16684503
## 174 0.02017356 62.52466 4.498633e-05 -0.19272946
## 175 0.02017356 62.50186 8.156964e-04 -0.82067666
## 176 0.02017356 62.49314 1.110571e-03 -0.95759297
## 177 0.02017356 62.49165 1.160844e-03 -0.97902709
## 178 0.02017356 62.51175 4.812388e-04 -0.63035927
## 179 0.02017356 62.51542 3.571989e-04 -0.54307879
## 180 0.02017356 62.48341 1.439434e-03 -1.09019391
## 181 0.01883796 62.52596 7.017734e-07  0.02492737
## 182 0.01883796 62.52113 1.530019e-04 -0.36806658
## 183 0.01883796 62.51233 4.304851e-04 -0.61738629
## 184 0.01883796 62.51768 2.620569e-04 -0.48169901
## 185 0.01883796 62.50563 6.417354e-04 -0.75379967
## 186 0.01883796 62.52131 1.475995e-04 -0.36151002
## 187 0.01883796 62.52306 9.237775e-05 -0.28599710
## 188 0.01883796 62.52563 1.109618e-05 -0.09912076
## 189 0.01883796 62.52305 9.272988e-05 -0.28654166
## 190 0.01883796 62.52372 7.154421e-05 -0.25168954
## 191 0.01883796 62.50958 5.174239e-04 -0.67686361
## 192 0.01883796 62.48621 1.253949e-03 -1.05370215
## 193 0.01883796 62.51602 3.143341e-04 -0.52756222
## 194 0.01883796 62.52500 3.100880e-05 -0.16569920
## 195 0.01883796 62.52292 9.656113e-05 -0.29240118
## 196 0.01883796 62.51977 1.960626e-04 -0.41665382
## 197 0.01883796 62.52551 1.492714e-05 -0.11496517
## 198 0.01883796 62.51988 1.924069e-04 -0.41275111
## 199 0.01883796 62.52598 2.130146e-07  0.01373354
## 200 0.01883796 62.52595 1.170371e-06 -0.03219138
## 201 0.01883796 62.49581 9.515619e-04 -0.91790232
## 202 0.01883796 62.51377 3.850573e-04 -0.58390285
## 203 0.01883796 62.50741 5.856951e-04 -0.72013470
## 204 0.01883796 62.52573 7.898879e-06 -0.08362972
## 205 0.01883796 62.50443 6.796905e-04 -0.77577102
## 206 0.01883796 62.52333 8.376103e-05 -0.27233216
## 207 0.01883796 62.50150 7.721991e-04 -0.82688020
## 208 0.01883796 62.49163 1.083046e-03 -0.97926746
## 209 0.01883796 62.48862 1.177991e-03 -1.02128968
## 210 0.01883796 62.52294 9.613480e-05 -0.29175496
## 211 0.01883796 62.50901 5.353605e-04 -0.68849551
## 212 0.01883796 62.52465 4.204336e-05 -0.19294194
## 213 0.01883796 62.50588 6.339520e-04 -0.74921443
## 214 0.01883796 62.51519 3.402823e-04 -0.54890551
## 215 0.01883796 62.51529 3.371387e-04 -0.54636421
## 216 0.01883796 62.51739 2.710468e-04 -0.48989168
## 217 0.01883796 62.46961 1.777288e-03 -1.25446003
## 218 0.01883796 62.45177 2.339167e-03 -1.43915811
## 219 0.01883796 62.49488 9.807976e-04 -0.93189641
## 220 0.01883796 62.46074 2.056472e-03 -1.34939575
## 221 0.01883796 62.51379 3.846488e-04 -0.58359305
## 222 0.01883796 62.47276 1.678005e-03 -1.21891813
## 223 0.01883796 62.48902 1.165559e-03 -1.01588639
## 224 0.01883796 62.47686 1.548657e-03 -1.17099647
## 225 0.01883796 62.50415 6.883997e-04 -0.78072535
## 226 0.01883796 62.50627 6.216611e-04 -0.74191606
## 227 0.01883796 62.47852 1.496388e-03 -1.15106542
## 228 0.01883796 62.46050 2.064170e-03 -1.35191890
## 229 0.01883796 62.47577 1.583031e-03 -1.18392080
## 230 0.01883796 62.49860 8.635569e-04 -0.87442672
## 231 0.01957311 62.47587 1.642874e-03 -1.18278076
## 232 0.01957311 62.45594 2.295624e-03 -1.39814590
## 233 0.01957311 62.28924 7.748965e-03 -2.56876258
## 234 0.01957311 62.42755 3.225406e-03 -1.65727411
## 235 0.01957311 62.42785 3.215518e-03 -1.65473186
## 236 0.01957311 62.48902 1.211881e-03 -1.01585591
## 237 0.01957311 62.41233 3.723768e-03 -1.78071087
## 238 0.01957311 62.37107 5.073891e-03 -2.07860844
## 239 0.01957311 62.38150 4.732753e-03 -2.00751615
## 240 0.01957311 62.45667 2.271690e-03 -1.39083822
## 241 0.01833919 62.50439 6.627015e-04 -0.77655838
## 242 0.01833919 62.47699 1.502917e-03 -1.16945248
## 243 0.01833919 62.32147 6.265575e-03 -2.38778712
## 244 0.01833919 62.40137 3.820286e-03 -1.86450300
## 245 0.01833919 62.47982 1.416051e-03 -1.13515364
## 246 0.01833919 62.51581 3.121898e-04 -0.53299671
## 247 0.01833919 62.45471 2.186114e-03 -1.41042994
## 248 0.01833919 62.30474 6.777415e-03 -2.48340285
## 249 0.01833919 62.42220 3.182252e-03 -1.70169785
## 250 0.01833919 62.45491 2.179930e-03 -1.40843372
## 251 0.01833919 62.50118 7.609225e-04 -0.83211887
## 252 0.01833919 62.40265 3.781092e-03 -1.85491385
## 253 0.01833919 62.25772 8.214655e-03 -2.73407109
## 254 0.01833919 62.36576 4.910549e-03 -2.11387915
## 255 0.01833919 62.40076 3.839020e-03 -1.86906892
## 256 0.01833919 62.47562 1.545032e-03 -1.18572477
## 257 0.01833919 62.45727 2.107394e-03 -1.38480321
## 258 0.01833919 62.32055 6.293861e-03 -2.39317089
## 259 0.01833919 62.48049 1.395600e-03 -1.12692676
## 260 0.01833919 62.46822 1.771759e-03 -1.26974785
## 261 0.01833919 62.47962 1.422415e-03 -1.13770156
## 262 0.01833919 62.44554 2.466966e-03 -1.49829304
## 263 0.01833919 62.28877 7.265470e-03 -2.57126594
## 264 0.01833919 62.33520 5.845747e-03 -2.30640270
## 265 0.01833919 62.44225 2.567776e-03 -1.52859942
## 266 0.01833919 62.50991 4.932501e-04 -0.66995977
## 267 0.01833919 62.47645 1.519568e-03 -1.17591300
## 268 0.01833919 62.32588 6.130689e-03 -2.36194504
## 269 0.01833919 62.42322 3.150918e-03 -1.69329917
## 270 0.01833919 62.46664 1.820164e-03 -1.28697590
## 271 0.01833919 62.52382 6.658368e-05 -0.24614954
## 272 0.01833919 62.48332 1.308706e-03 -1.09128017
## 273 0.01833919 62.46617 1.834638e-03 -1.29208262
## 274 0.01833919 62.47673 1.510969e-03 -1.17258111
## 275 0.01833919 62.46551 1.855051e-03 -1.29925090
## 276 0.01833919 62.50626 6.051976e-04 -0.74210227
## 277 0.01833919 62.44466 2.493988e-03 -1.50647637
## 278 0.01833919 62.33812 5.756483e-03 -2.28872579
## 279 0.01833919 62.44460 2.495791e-03 -1.50702079
## 280 0.01833919 62.45170 2.278344e-03 -1.43987492
## 281 0.01833919 62.50728 5.739984e-04 -0.72272070
## 282 0.01833919 62.50439 6.624950e-04 -0.77643740
## 283 0.01833919 62.42191 3.191050e-03 -1.70404856
## 284 0.01833919 62.45668 2.125476e-03 -1.39073140
## 285 0.01833919 62.45532 2.167282e-03 -1.40434205
## 286 0.01833919 62.51137 4.483422e-04 -0.63873392
## 287 0.01833919 62.49021 1.097447e-03 -0.99932540
## 288 0.01833919 62.43564 2.770378e-03 -1.58775917
## 289 0.01833919 62.49883 8.330408e-04 -0.87065939
## 290 0.01833919 62.47377 1.601760e-03 -1.20729614
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## 674 0.01887719 62.52571 8.553580e-06  0.08693437
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## 872 0.02040151 62.51731 2.969073e-04  0.49229766
## 873 0.02040151 62.47742 1.660921e-03  1.16437199
## 874 0.02040151 62.51675 3.160513e-04  0.50792096
## 875 0.02040151 62.47801 1.640512e-03  1.15719617
## 876 0.02040151 62.52056 1.855052e-04  0.38913060
## 877 0.02040151 62.49689 9.950703e-04  0.90124779
## 878 0.02040151 62.36682 5.438051e-03  2.10687593
## 879 0.02040151 62.48305 1.468160e-03  1.09472236
## 880 0.02040151 62.43442 3.130267e-03  1.59848290
## 881 0.02040151 62.52408 6.519137e-05  0.23068129
## 882 0.02040151 62.52297 1.030907e-04  0.29008616
## 883 0.02040151 62.46972 1.923973e-03  1.25318984
## 884 0.02040151 62.50625 6.749473e-04  0.74225348
## 885 0.02040151 62.46891 1.951684e-03  1.26218232
## 886 0.02040151 62.51889 2.427644e-04 -0.44515353
## 887 0.02040151 62.46921 1.941351e-03 -1.25883671
## 888 0.02040151 62.38120 4.947351e-03 -2.00957253
## 889 0.02040151 62.45029 2.587834e-03 -1.45340127
## 890 0.02040151 62.52026 1.959335e-04 -0.39991863
predicted_trans2 %>% 
  ggplot(aes(factor(month, levels = month.abb), .resid, group = year)) + 
  geom_hline(yintercept = 0, colour = "white", size = 3) +
  geom_line() + 
  facet_wrap(~ area)

For some apartement size classes, few years may have large influence on average number of transactions. We can look at the large cook’s distance.

predicted_trans2 %>% 
  arrange(desc(.cooksd)) %>% 
  dplyr::select(.cooksd, everything()) %>% 
  head()
##      .cooksd transactions month year     area  .fitted  .se.fit   .resid
## 1 0.02066502          530   Nov 2005 41-54,99 285.0741 9.243226 244.9259
## 2 0.01732572          512   Oct 2005 41-54,99 284.8125 9.129342 227.1875
## 3 0.01672219          461   Nov 2005 55-69,99 240.6752 9.243226 220.3248
## 4 0.01662042          457   Dec 2005 55-69,99 237.3466 9.243226 219.6534
## 5 0.01563057          492   Aug 2005 41-54,99 276.2125 9.129342 215.7875
## 6 0.01429830          443   Sep 2005 55-69,99 236.6136 9.129342 206.3864
##         .hat   .sigma .std.resid
## 1 0.02187882 61.96100   3.963025
## 2 0.02134301 62.04045   3.675001
## 3 0.02187882 62.06920   3.564966
## 4 0.02187882 62.07199   3.554102
## 5 0.02134301 62.08812   3.490594
## 6 0.02134301 62.12556   3.338521

Same for mean price per m^2:

predicted_pua2 <- harju %>% 
  lm(price_unit_area_mean ~ month + year + area, data = .) %>% 
  augment 
predicted_pua2 %>% 
  ggplot(aes(factor(month, levels = month.abb), .resid, group = year, color = factor(year))) + 
  geom_hline(yintercept = 0, colour = "white", size = 3) +
  geom_line() + 
  facet_wrap(~ area) +
  scale_color_viridis(discrete = TRUE) +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5))

Seems ok!

predicted_pua2 %>%
  arrange(desc(.cooksd)) %>% 
  dplyr::select(.cooksd, everything(.)) %>% 
  head()
##       .cooksd price_unit_area_mean month year     area  .fitted  .se.fit
## 1 0.009230944              1725.98   Apr 2007 10-29,99 1043.973 34.24826
## 2 0.008394703               421.50   Jul 2009 10-29,99 1093.030 33.20911
## 3 0.007883079              1650.16   Jun 2007 30-40,99 1019.909 34.24826
## 4 0.006989624              1665.78   Aug 2007 10-29,99 1072.318 34.24826
## 5 0.006803107              1604.90   Apr 2007 30-40,99 1019.410 34.24826
## 6 0.006686472              1615.97   Apr 2007 41-54,99 1035.521 34.24826
##      .resid       .hat   .sigma .std.resid
## 1  682.0070 0.01950485 244.2558   2.808659
## 2 -671.5304 0.01833919 244.2911  -2.763871
## 3  630.2512 0.01950485 244.4184   2.595517
## 4  593.4616 0.01950485 244.5261   2.444009
## 5  585.4899 0.01950485 244.5485   2.411179
## 6  580.4493 0.01950485 244.5626   2.390421

Robust lm fit to number of transactions. Play with weights: price_min, price_unit_area_mean etc..

# install.packages("MASS")
library(MASS)
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
predicted_transa_robust <- harju %>% 
  rlm(transactions ~ month + area, data = ., weights = price_min) %>% 
  augment

Add robust fit to plot:

p + geom_line(data = predicted_transa, aes(month, .fitted, group = 1), 
              color = "red",
              size = 1) + 
  geom_line(data = predicted_transa_robust, aes(month, .fitted, group = 1), 
            color = "blue",
            size = 1) +
  labs(caption = "Red line: model fit of seasonal effect to number of transactions.\nBlue line: robust model fit of seasonal effect to number of transactions, weighted for minimal price. \nSource: Estonian Land Board, transactions database.")

## Whole dataset: all counties

Plot whole dataset:

apartments %>% 
  ggplot(aes(date, transactions, group = area, color = area)) +
  geom_line() +
  facet_wrap(~ county, scales = "free_y")

apartments %>% 
  mutate(price_unit_area_mean = price_unit_area_mean / consumerindex) %>% 
  ggplot(aes(date, price_unit_area_mean, group = area, color = area)) +
  geom_line() +
  facet_wrap(~ county, scales = "free_y")
## Warning: Removed 8 rows containing missing values (geom_path).

Fit multiple models

Fit model for each county. Goodness of model fit is evaluated by its ability to predict response values. Response values can be predicted using the same data that was used to train model. In this case we are dealing with in-sample analysis, which is ok when all we want to know is model coeficients (eg. intercept and slope) to describe present data. In cases when we want to predict using some unseen future data, such models are usually overfitted, overly optimistic and don’t perform very well. To manage overfitting, we split dataset into training set for model fitting and test set for model performance assessment.

Resampling can be performed very well using base R function sample(). Let’s say we want to use approx. 70% of rows from “mtcars” table to be used in model training and leave remaining 30% for model testing. Basically, all we need to do is to generate to non-overlapping row indexes.

set.seed(123)
index <- sample(1:nrow(mtcars), floor(0.7 * nrow(mtcars)), replace = FALSE)
index
##  [1] 10 25 13 26 27  2 14 23 29 11 22 32 24 31 28 16  4  1  5 30 19  8
## ~70% data goes to training set
train <- mtcars[index, ]
## remaining ~30% will be used for testing model performance
test <- mtcars[-index, ]

Index based resampling is also implemented in tidyverse. We can use resample_partition() function from “modelr” library to perform. Here we generate data splits and move them to separate columns.

library(modelr)
## 
## Attaching package: 'modelr'
## The following object is masked from 'package:broom':
## 
##     bootstrap
## Generate data splits and move into separate columns
trans <- apartments %>%
  group_by(county) %>%
  nest %>% 
  mutate(parts = map(data, ~resample_partition(.x, c(test = 0.3, train = 0.7))),
         test = map(parts, "test"),
         train = map(parts, "train")) %>% 
  dplyr::select(-parts)

Fit model to each data split. Let’s start with number of transactions.

## Fit model
trans <- trans %>%
  mutate(mod_train = map(train, ~lm(transactions ~ month + area, data = .x)))
## Print data with new model column
trans %>% 
  dplyr::select(mod_train, everything())
## # A tibble: 15 x 5
##    mod_train             county                data           test
##       <list>              <chr>              <list>         <list>
##  1  <S3: lm>      Harju maakond <tibble [890 x 18]> <S3: resample>
##  2  <S3: lm>       Hiiu maakond <tibble [400 x 18]> <S3: resample>
##  3  <S3: lm>   Ida-Viru maakond <tibble [890 x 18]> <S3: resample>
##  4  <S3: lm>     Jõgeva maakond <tibble [798 x 18]> <S3: resample>
##  5  <S3: lm>      Järva maakond <tibble [824 x 18]> <S3: resample>
##  6  <S3: lm>      Lääne maakond <tibble [832 x 18]> <S3: resample>
##  7  <S3: lm> Lääne-Viru maakond <tibble [884 x 18]> <S3: resample>
##  8  <S3: lm>      Põlva maakond <tibble [738 x 18]> <S3: resample>
##  9  <S3: lm>      Pärnu maakond <tibble [889 x 18]> <S3: resample>
## 10  <S3: lm>      Rapla maakond <tibble [797 x 18]> <S3: resample>
## 11  <S3: lm>      Saare maakond <tibble [786 x 18]> <S3: resample>
## 12  <S3: lm>      Tartu maakond <tibble [890 x 18]> <S3: resample>
## 13  <S3: lm>      Valga maakond <tibble [847 x 18]> <S3: resample>
## 14  <S3: lm>   Viljandi maakond <tibble [875 x 18]> <S3: resample>
## 15  <S3: lm>       Võru maakond <tibble [832 x 18]> <S3: resample>
## # ... with 1 more variables: train <list>

coef() and summary() return vector and S3 object respectively. Model coeficients and summary statistics can be returned as a data frame using tidy() function from “broom” library:

## model coeficients
trans %>% 
  mutate(mod_tidy = map(mod_train, tidy)) %>% 
  dplyr::select(county, mod_tidy) %>% 
  unnest %>% 
  head()
## # A tibble: 6 x 6
##          county        term   estimate std.error  statistic      p.value
##           <chr>       <chr>      <dbl>     <dbl>      <dbl>        <dbl>
## 1 Harju maakond (Intercept)  90.720597  10.95902  8.2781703 7.956235e-16
## 2 Harju maakond    monthAug   8.425303  12.99468  0.6483655 5.169934e-01
## 3 Harju maakond    monthDec   7.407290  12.87110  0.5754980 5.651675e-01
## 4 Harju maakond    monthFeb -19.712457  13.36976 -1.4744058 1.408899e-01
## 5 Harju maakond    monthJan -34.256393  12.75323 -2.6860961 7.426733e-03
## 6 Harju maakond    monthJul -11.766739  13.05168 -0.9015499 3.676530e-01

Pseudo out-of-sample model performance, augment() adds predictions to original data frame (.fitted). We subtract fitted values from the original values and calculate root-mean-squared deviation (rmsd). Smaller rmsd indicates better fit.

trans <- trans %>%
  mutate(mod_pred = map2(mod_train, test, ~augment(.x, newdata = .y)),
         mod_pred = map(mod_pred, ~mutate(.x, .resid = transactions - .fitted)),
         mod_rmsd = map_dbl(mod_pred, ~sqrt(mean(.x$`.resid`^2)))) 
trans %>% 
  dplyr::select(county, mod_rmsd) %>% 
  arrange(desc(mod_rmsd))
## # A tibble: 15 x 2
##                county   mod_rmsd
##                 <chr>      <dbl>
##  1      Harju maakond 66.4419493
##  2      Tartu maakond 16.5692863
##  3   Ida-Viru maakond  9.7488850
##  4      Pärnu maakond  9.2678223
##  5 Lääne-Viru maakond  4.8961802
##  6   Viljandi maakond  3.5521556
##  7      Järva maakond  3.1063724
##  8      Rapla maakond  2.9415115
##  9      Valga maakond  2.9113005
## 10      Lääne maakond  2.7434744
## 11      Saare maakond  2.5359518
## 12     Jõgeva maakond  2.4825984
## 13       Võru maakond  2.3033747
## 14      Põlva maakond  1.9872345
## 15       Hiiu maakond  0.7937306

We can see that Harju county displays worst fit and Tartu is next. These two counties show also majority of transactions.

trans_pred <- trans %>% 
  dplyr::select(county, mod_pred) %>% 
  unnest
trans_pred %>% 
  dplyr::select(.fitted, transactions, everything()) %>% 
  head()
## # A tibble: 6 x 22
##    .fitted transactions        county       date  year month     area
##      <dbl>        <int>         <chr>     <date> <int> <chr>    <chr>
## 1 136.5889          175 Harju maakond 2005-02-01  2005   Feb 30-40,99
## 2 221.3443          257 Harju maakond 2005-02-01  2005   Feb 41-54,99
## 3 244.3975          350 Harju maakond 2005-03-01  2005   Mar 41-54,99
## 4  90.7206          101 Harju maakond 2005-04-01  2005   Apr 10-29,99
## 5 241.0568          360 Harju maakond 2005-04-01  2005   Apr 41-54,99
## 6 199.9944          329 Harju maakond 2005-04-01  2005   Apr 55-69,99
## # ... with 15 more variables: area_total <dbl>, area_mean <dbl>,
## #   price_total <int>, price_min <dbl>, price_max <dbl>,
## #   price_unit_area_min <dbl>, price_unit_area_max <dbl>,
## #   price_unit_area_median <dbl>, price_unit_area_mean <dbl>,
## #   price_unit_area_sd <dbl>, title <chr>, subtitle <chr>,
## #   consumerindex <dbl>, .se.fit <dbl>, .resid <dbl>